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Quantum Mechanics

Quantum Mechanics Courses - Quantum Physics Courses (Text, Images, Videos/Movies & Audio/Sound) Quantum Mechanics - Quantum Physics Courses (Text & Images) Quantum Mechanics & Quantum Physics Teaching Modules (Calculators, Applets, Animations, Simulations & Videos/Movies) Bohr ~ Schrödinger ~ Hamiltonian ~ Heisenberg ~ Fermi Atomic Quantum Mechanics ~ Coherent States of Quantum Harmonics Hilbert Curves, Sierpinski Curves, Peano Curves Kronig-Penny Model ~ Quantum Monty Hall Quantum Interference ~ Quantum Barrier Penetration/Quantum Tunneling

Quantum Mechanics Calculators, Applets & Simulations QUANTUM MECHANICS - QUANTUM PHYSICS COURSES WITH TEXT, IMAGES, VIDEOS/MOVIES & AUDIO/SOUND Undergraduate Quantum Mechanics - Quantum Physics Courses QUANTUM PHYSICS (PHYSICS 130A) (QUICKTIME) - J. Branson, High Energy Physics, Department of Physics, University of California, San Diego (UCSD) Multimedia Quantum Physics Course 130A (Text, Images, Videos/Movies & Audio/Sound). VERY VERY VERY...EXTENSIVE. Examples of Quantum Physics Course 130A, 130B & 13C Subject Categories for Quantum Physics Video Lectures & Quantum Physics Textbook include "...Problems with Classical Physics Video Lectures; Thought Experiments on Diffraction Video Lectures; Wave Packets and Uncertainty Video Lectures; Operators Video Lectures; Eigenfunctions, Eigenvalues and Vector Spaces Video Lectures; Delta Function Potentials in One Dimension Video Lectures; Harmonic Oscillator Solution with Operators Video Lectures; Angular Momentum Video Lectures; Matrix Representation of Operators and States Video Lectures; Quantum Mechanics in an Electromagnetic Field Video Lectures; Time Independent Perturbation Theory Video Lectures; Classical Field Theory Video Lectures; The Classical Electromagnetic Field Video Lectures; Quantization of the EM Field Video Lectures; etc..." For more information see UCSD Physics Video on Demand; Jim Branson's Home Page; High Energy Physics or the Department of Physics QUANTUM PHYSICS (PHYSICS 130B) (QUICKTIME) - J. Branson, High Energy Physics, Department of Physics, University of California, San Diego (UCSD) Multimedia Quantum Physics Course 130B (Text, Images, Videos/Movies & Audio/Sound). VERY VERY VERY...EXTENSIVE. For more information see UCSD Physics Video on Demand; Jim Branson's Home Page; High Energy Physics or the Department of Physics QUANTUM PHYSICS (PHYSICS 130C) (QUICKTIME) - J. Branson, High Energy Physics, Department of Physics, University of California, San Diego (UCSD) Multimedia Quantum Physics Course 130C (Text, Images, Videos/Movies & Audio/Sound). VERY VERY VERY...EXTENSIVE. For more information see UCSD Physics Video on Demand; Jim Branson's Home Page; High Energy Physics or the Department of Physics QUANTUM MECHANICS (137A) (REAL PLAYER) - Raphael Bousso, Department of Physics, Division of Mathematical & Physical Sciences, College of Letters & Science, University of California, Berkeley Multimedia Quantum Mechanics Course (Text, Images, Videos/Movies & Audio/Sound). VERY VERY VERY...EXTENSIVE. Examples from over "30" Quantum Mechanics Video Lectures include "...Bound States Video Lecture; Determinant States Video Lecture; Particles and State Video Lectures; Angular Wave Function Video Lecture; Angular Momentum Video Lecture; Spin Video Lecture; Magnetism Video Lecture; Quantum Numbers and Electrons Video Lecture; etc..." For more information see Department of Physics; Fall 2007 Courses; Courses or Berkeley Webcasts INTRODUCTION TO QUANTUM MECHANICS II (QUICKTIME & REAL PLAYER) - R.W. Field, Department of Chemistry, & the MIT OpenCourseWare, MIT Multimedia Introduction to Quantum Mechanics II Course (Text, Images, Videos/Movies & Audio/Sound). VERY VERY VERY...EXTENSIVE. Introduction to Quantum Mechanics II "...course covers time-dependent quantum mechanics and spectroscopy. Topics include perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, and nonlinear spectroscopy..." Examples of Introduction to Quantum Mechanics II Video Lectures include: "...Introduction to the Spectroscopic Effective Hamiltonian: The Born-Oppenheimer approximation and matrix elements of terms in the effective molecular Hamiltonian that violate the BO approximation. Vibration, rotation, spin-orbit, interelectronic interaction. Hund's coupling cases Video Lectures; Spectroscopic Pertubations, Predissociation, and Autoionization: Introduction to dynamical processes Video Lectures; Semiclassical Methods for Calculating Vibrational Overlap Integrals Video Lectures; etc..." Examples of Introduction to Quantum Mechanics II Lectures (PDF) include: "...Quantum Dynamics; Time-Evolution Operator; Time-development of State Amplitudes/Resonant Driving of Two-Level System; Perturbation Theory; Fermi's Golden Rule; Irreversible Relaxation; etc..." For more information see Introduction to Quantum Mechanics II Home Page; Robert W. Field's Home Page; Department of Chemistry; Chemistry Courses or MIT OpenCourseWare QUANTUM MECHANICS - QUANTUM PHYSICS COURSES Undergraduate Quantum Mechanics - Quantum Physics Courses QUANTUM MECHANICS I (PHYSICS 521) - M. Breinig, Department of Physics & Astronomy, College of Arts & Sciences, University of Tennessee Multimedia Quantum Mechanics Course (Text, Images, Animations & Simulations). VERY VERY VERY...EXTENSIVE. Examples of Quantum Mechanics Chapters include: "...The Fundamental Assumptions of Quantum Mechanics; Square Potentials; Mathematical Foundations; The Postulates of Quantum Mechanics; Representations; The Density Matrix; The WKB Approximation; The Harmonic Oscillator; Two-Level Systems (A Spin 1/2 particle); Angular Momentum; etc..." For more information see Quantum Mechanics Home Page (PHYSICS 521); Marianne Breinig's Home Page or the Department of Physics & Astronomy QUANTUM PHYSICS (PHYS2041) - PDF - Z. Ficek, Department of Physics, School of Physical Sciences, University of Queensland, Brisbane, Australia Multimedia Quantum Physics Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of Quantum Physics Chapters include: "...Radiation (Light) is a Wave; Difficulties of the Wave Theory of Radiation; Black-Body Radiation; Planck's Quantum Hypothesis; The Foundations of the Quantum Theory; The Bohr Model; Duality of Light and Matter; Non-relativistic Schrödinger Equation; Applications of the Schrödinger Equation: Potential (Quantum) Wells; Multi-Dimensional Quantum Wells: Quantum Wires and Quantum Dots; Linear Operators and Their Algebra; Dirac Notation; Matrix Representations; Time-Independent Perturbation Theory; Quantum Harmonic Oscillator; etc..." For more information see Teaching; Zbigniew Ficek's Home Page or the Department of Physics QUANTUM MECHANICS II - Klaus Schulten, Theoretical and Computational Biophysics Group, Department of Physics, University of Illinois, Urbana-Champaign, Illinois Multimedia Quantum Mechanics II Course - PDF (Text & Images). VERY VERY VERY...EXTENSIVE. Examples from over "11" Quantum Mechanics II Lectures "...Lagrangian Mechanics; Path Integral Formulation of Quantum Mechanics; Quantum Harmonic Oscillator; Angular Momentum and Spin; Motion in Spherically Symmetric Potentials; Many-Particle Systems; Spinor Formulation of Relativistic Quantum Mechanics; etc..." For more information see Quantum Mechanics II Home Page; Klaus Schulten's Home Page or the Department of Physics INTERMEDIATE QUANTUM MECHANICS - R. Fitzpatrick, Department of Physics, University of Texas, Austin, Texas Multimedia Intermediate Quantum Mechanics Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of Quantum Mechanics Lectures include: "...Probability Theory; Wave-particle Duality; Fundamentals of Quantum Mechanics; One-dimensional Potentials; Multi-particle Systems; Three-dimensional Quantum Mechanics; Orbital Angular Momentum; Central Potentials; Spin Angular Momentum; Addition of Angular Momentum; Time-independent Perturbation Theory; Time-dependent Perturbation Theory; etc..." For more information see the Quantum Mechanics Home Page; Courses taught by Richard Fitzpatrick at UT Austin; Richard Fitzpatrick's Home Page or the Department of Physics ADVANCED QUANTUM PHYSICS (PDF) - David Ritchie, Department of Physics, Cavendish Laboratory, University of Cambridge Multimedia Quantum Physics Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples from over "23" Quantum Mechanics Lectures include: Lectures 1-4: Review of Quantum Physics; Lectures 5-8: Methods of Approximation "...Variational Method; Born-Oppenheimer Approximation; Time-independent Perturbation Theory; Degenerate Perturbation Theory..." Lectures 9-12: Relativity and Magnetic fields "...Quantum Mechanics and Magnetic Fields; Relativistic Quantum Mechanics; Particle in a Uniform Magnetic Field; Landau Levels..." For more information see the Undergraduate Teaching or the Department of Physics ADVANCED QUANTUM MECHANICS (PH195C) - H. Mabuchi, Department of Applied Physics, Stanford University Multimedia Quantum Mechanics Course - PDF (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of Quantum Mechanics Chapters include: "...Eigenvalues of a Density Operator; Entanglement & Information; The Bloch Equations; Eigenfunctions of the Harmonic Oscillator; etc..." For more information see the MabuchiLab or the Department of Physics; ADVANCED QUANTUM MECHANICS: THE PATH INTEGRAL APPROACH TO QUANTUM MECHANICS LECTURE NOTES - Matthias Blau, Gravity and String Theory Group, Institut de Physique, Université de Neuchâtel, Switzerland Multimedia Advanced Quantum Mechanics: The Path Integral Approach to Quantum Mechanics Course Lecture Notes - PDF - 55 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Advanced Quantum Mechanics: The Path Integral Approach to Quantum Mechanics Notes Chapters include "...The Evolution Kernel; Towards the Path Integral Representation of the Kernel; Gaussian Path Integrals and Determinants; Generating Functionals and Perturbative Expansions; etc..." For more information see Matthias Blau's Lecture Notes; Matthias Blau's Home Page; Gravity and String Theory Group or the Institut de Physique Graduate Quantum Mechanics - Quantum Physics Courses QUANTUM MECHANICS - R. Fitzpatrick, Department of Physics, University of Texas, Austin, Texas Multimedia Graduate Quantum Mechanics Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of Quantum Mechanics Chapters include: "...Position and Momentum; Quantum Dynamics; Angular Momentum; Approximation Methods; Scattering Theory; etc..." For more information see the Quantum Mechanics Home Page; Courses taught by Richard Fitzpatrick at UT Austin; Richard Fitzpatrick's Home Page or the Department of Physics Undergraduate Quantum Mechanics in Chemistry Textbooks QUANTUM MECHANICS IN CHEMISTRY (PDF) - Authors: Jack Simons and Jeff Nichols; Henry Eyring Center for Theoretical Chemistry, Department of Chemistry, University of Utah Multimedia Quantum Mechanics in Chemistry Textbook (Text & Images). VERY VERY VERY...EXTENSIVE. Quantum Mechanics in Chemistry "...This is a text dealing with the basics of quantum mechanics and electronic structure theory. It provides an introduction to molecular spectroscopy (although most classes on this subject will require additional material) and to the subject of molecular dynamics (whose classes again will require additional material)..." Examples of Quantum Mechanics in Chemistry Sections, Chapters & Subchapters include: Section 1: Basic Tools of Quantum Mechanics Chapter 1: Quantum mechanics describes matter in terms of wavefunctions and energy levels. physical measurements are described in terms of operators acting on wavefunctions; Chapter 2: Approximation methods can be used when exact solutions to the Schrödinger equation can not be found; Chapter 3: Application of the Schrödinger equation to the motions of electrons and nuclei in a molecule lead to the chemists' picture of electronic energy surfaces on which vibration and rotation occurs and among which transitions take place; Subchapter 1: Born-Oppenheimer Separation of Electronic and Nuclear Motions; Subchapter 2: Rotation and Vibration of Diatomic Molecules; Section 2: Simple Molecular Orbital Theory; Section 3: Electronic Configurations, Term Symbols, and States; Section 4: Molecular Rotation and Vibration; etc. For more information see Theoretical Chemistry; Jack Simons Home Page or the Henry Eyring Center for Theoretical Chemistry Undergraduate Quantum Mechanics in Chemistry Courses INTRODUCTION TO QUANTUM MECHANICS I - T. Van Voorhis, Department of Chemistry, & the MIT OpenCourseWare, MIT Multimedia Introduction to Quantum Mechanics I Course (Text & Images). VERY VERY VERY...EXTENSIVE. Introduction to Quantum Mechanics I "...covers fundamental concepts of quantum mechanics: wave properties, uncertainty principles, Schrödinger equation, and operator and matrix methods. Basic applications of the following are discussed: one-dimensional potentials (harmonic oscillator), three-dimensional centrosymmetric potentials..." Examples of Introduction to Quantum Mechanics I Lectures include: "...Experimental Evidence for Quantum Mechanics; The Machinery of Quantum Mechanics; Exactly Solvable Problems; Matrix Mechanics; Time Dependence; Angular Momentum; Central Potentials; etc..." For more information see Introduction to Quantum Mechanics I Home Page; Troy Van Voorhis's Home Page; Department of Chemistry; Chemistry Courses or MIT OpenCourseWare INTRODUCTION TO QUANTUM MECHANICS II (QUICKTIME & REAL PLAYER) - R.W. Field, Department of Chemistry, & the MIT OpenCourseWare, MIT Multimedia Introduction to Quantum Mechanics II Course (Text, Images, Videos/Movies & Audio/Sound). VERY VERY VERY...EXTENSIVE. Introduction to Quantum Mechanics II "...course covers time-dependent quantum mechanics and spectroscopy. Topics include perturbation theory, two-level systems, light-matter interactions, relaxation in quantum systems, correlation functions and linear response theory, and nonlinear spectroscopy..." Examples of Introduction to Quantum Mechanics II Video Lectures include: "...Introduction to the Spectroscopic Effective Hamiltonian: The Born-Oppenheimer approximation and matrix elements of terms in the effective molecular Hamiltonian that violate the BO approximation. Vibration, rotation, spin-orbit, interelectronic interaction. Hund's coupling cases Video Lectures; Spectroscopic Pertubations, Predissociation, and Autoionization: Introduction to dynamical processes Video Lectures; Semiclassical Methods for Calculating Vibrational Overlap Integrals Video Lectures; etc..." Examples of Introduction to Quantum Mechanics II Lectures (PDF) include: "...Quantum Dynamics; Time-Evolution Operator; Time-development of State Amplitudes/Resonant Driving of Two-Level System; Perturbation Theory; Fermi's Golden Rule; Irreversible Relaxation; etc..." For more information see Introduction to Quantum Mechanics II Home Page; Robert W. Field's Home Page; Department of Chemistry; Chemistry Courses or MIT OpenCourseWare Undergraduate Quantum Chemistry Lectures QUANTUM CHEMISTRY - C.D. Sherrill, Physical Chemistry Program, School of Chemistry, College of Sciences, University of Georgia Multimedia Quantum Chemistry Lectures (Text & Images). VERY VERY EXTENSIVE. Examples of Quantum Chemistry Lectures Subject Categories include: The Motivation for Quantum Mechanics Mathematical Background: Operators, Commutators in Quantum Mechanics; etc.; Schrödinger Equation; Postulates of Quantum Mechanics; Perturbation Theory; Molecular Quantum Mechanics; etc..." For more information see C. David Sherrill's Home Page or the School of Chemistry

QUANTUM MECHANICS TEACHING MODULES WITH CALCULATORS, APPLETS, VIDEOS/MOVIES QUANTUM PHYSICS TEACHING MODULES WITH CALCULATORS & APPLET AN INTRODUCTION TO QUANTUM MECHANICS (CHIME & FLASH) - N. McDonald, M. Kitagawa-DeLeon, A. Timasheva, H. Hanlin, Z. Lilas, & S.J. Singer, Department of Chemistry, Ohio State University Multimedia Quantum Mechanics Teaching Modules (Text, Images, Animations & Simulations). VERY VERY EXTENSIVE. Examples of Quantum Mechanics Teaching Modules include: "...Uncertainty; Probability; Trajectories and Probability; Particles and Waves; Stationary States; Nodes and DeBroglie's Principle; Nodes of the Hydrogen Atom Eigenstates; The Helium Wave Function; The Pauli Principle; The Aufbau Principle; etc..." For more information see BETHA Chemistry Tutorials or the Department of Chemistry INTRODUCTION TO QUANTUM MECHANICS: A TIME-DEPENDENT PERSPECTIVE (QUICKTIME) - D. Tannor, Department of Chemical Physics, Faculty of Chemistry, Weizmann Institute of Science, Rehovot, Israel Multimedia Quantum Mechanics Teaching Modules (Text, Images, Animations & Simulations). VERY EXTENSIVE. Examples of Quantum Mechanics Subject Categories include "...Formal Theory & Methods of Approximation; Applications; Pictures & Concepts For more information see Introduction to Quantum Mechanics: A Time-Dependent Perspective Home Page; David Tannor's Home Page or the Department of Chemical Physics PATH INTEGRALS IN QUANTUM MECHANICS (JAVA APPLET) - Arcadi Santamaria, Departament de Física Teòrica, Universitat de València, Spain VERY EXTENSIVE. Path Integrals in Quantum Mechanics Calculator "...is a demonstration of the numerical computation of path integrals in quantum mechanics..." For more information see the Departament de Física Teòrica QUANTUM PHENOMENA SIMULATIONS - Physics Education Technology, Department of Physics, College of Arts & Sciences, University of Colorado Multimedia Physics Simulations Teaching Modules (Text & Images). VERY VERY EXTENSIVE. Examples of Quantum Phenomena Simulations include "...Quantum Tunneling and Wave Packets; Quantum Bound State; Quantum Wave Interference; Stern-Gerlach Experiment; Double Wells and Covalent Bonds; etc..." For more information see Interactive Physics Simulations; Physics Education Technology or the Department of Physics VIRTUAL QUANTUM MECHANICS (JAVA APPLETS) - O. Tchernyshyov & J. Wasserman, Department of Physics & Astronomy, Johns Hopkins University VERY VERY EXTENSIVE. Multimedia Quantum Mechanics Teaching Modules (Text & Images). For more information see Oleg Tchernyshyov's Home Page or the Department of Physics & Astronomy Some examples from over "6" Quantum Mechanics Applets include Entangled Spins and Quantum Encryption Potts Model Simulation Applet Cylindrical Coordinates Visualization Applet VISUAL QUANTUM MECHANICS (SHOCKWAVE) - Physics Education Research Group, Department of Physics, Kansas State University Multimedia Quantum Mechanics Teaching Modules (Text, Images, Animations & Simulations). VERY VERY EXTENSIVE. For more information see the Physics Education Research Group or the Department of Physics Some examples of Quantum Mechanics Shockwave Simulations include Franck-Hertz Experiment Zeeman Spectroscopy Cylindrical Coordinates Visualization Applet VISUAL QUANTUM MECHANICS (QUICKTIME) - Bernd Thaller, Institute for Mathematics & Scientific Computing, Karl-Frazens-Universität Graz, Austria In English & German/Deutsch. Multimedia Quantum Mechanics Teaching Modules (Text, Images & Videos/Movies). VERY VERY EXTENSIVE. Examples of Quantum Mechanics Video Teaching Modules include: Free motion "...Direction of motion in 1D Video; Superposition of Gaussian states in 2D Video; etc..." Boundary conditions "...Unit function in a Dirichlet box Video; Double-slit experiment Video; etc...." Harmonic Oscillator "...Squeezed state in 2D Video; Constant shape of a shifted eigenstate Video; etc..." Special Systems "...Free fall of a Gaussian; Gaussian in a constant magnetic field; Aharonov-Bohm effect Video..." Scattering "...Potential step in momentum space Video; Tunneling through a barrier Video; Scattering at a cylindrical barrier Video; etc..." Advanced Quantum Mechanics Video Teaching Modules include: Hydrogen Atom "...Superposition state Video; Oscillation Video; etc..." Dirac Equation "...Zitterbewegung (free motion) Video; Lorentz transformation Video; Smooth potential well (positive energy) Video; Smooth potential well (negative energy) Video; Scattering at a high potential step; Scattering at a very high step (Klein's paradox) Video; etc..." For more information see the Visual Quantum Mechanics WAVE PACKETS AND THE CLASSICAL LIMIT OF QUANTUM MECHANICS - Carlos R. Stroud, Jr., Institute of Optics, University of Rochester Multimedia Wave Packet Teaching Modules (Text, Images, Animations & Simulations). VERY VERY EXTENSIVE. Wave Packet Teaching Modules Subject Categories & Animations include: Circular Orbit Wave Packets "...Motion of a hydrogen circular orbit wave packet; Strobed motion of a circular orbit wave packet; Spreading of a hydrogen circular orbit wave packet; etc..." Core Scattering "...Core Scattering in Elliptic States: Hydrogen vs. Sodium; Core Scattering in Sodium: Classical vs. Hydrogenic Behavior..." Infinite Square Well Wave Packets "...Gaussian Wave Packet; Decay of High Momentum Wave Packet; etc..." Terahertz Pulses "...Shaping of a Terahertz Pulse by a Slit in a Thin Screen; Shaping of a Terahertz Pulse by a Slit in a Thick Screen..." For more information see Stroud Wave Packet Home Page or the Institute of Optics

BOHR CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS THE BOHR ATOM (HYDROGEN ATOM) CALCULATORS & APPLETS THE BOHR ATOM: ENERGY LEVELS OF THE HYDROGEN ATOM (JAVA APPLET) - G. Anderson, Department of Physics & Astronomy, Northwestern University For more information see The Virtual Physics Laboratory; Undergraduate Physics or the Department of Physics & Astronomy HYDROGEN ATOM ORBITAL VIEWER (JAVA APPLET) - P. Falstad VERY EXTENSIVE. Hydrogen Atom Orbital Calculator "...displays the wave functions (orbitals) of the hydrogen atom (actually the hydrogenic atom) in 3-D..." Hydrogen Atom Orbital Calculator INPUT Values include: "...Select Real Orbitals; Complex Orbitals; Real Combinations; Complex Combinations; Multiple Bases or Hybrid Bases; Show No Slicing, X Slicing, Y Slicing or Z Slicing; etc..." For more information see Math, Physics & Engineering Applets or Paul Falstad's Home Page HYDROGEN ATOM PROBABILITY DENSITY APPLET - C. Fisher, Department of Physics, Davidson College Hydrogen Atom Probability Density Calculator "...solves the Quantum Mechanical Hydrogenic Wave Function and then paints a picture showing the amplitude of Psi in the x-z plane a certain number of Bohr radii from the nucleus. The reason the Applet graphs the amplitude of Psi instead of the modulus squared (the actual probability of finding the electron an x number of Bohr radii from the nucleus) is due to limitations in the color scale..." For more information see Cabell Fisher's Home Page or Department of Physics SCHRÖDINGER CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS SCHRÖDINGER'S EQUATION CALCULATORS & APPLETS 1-DIMENSIONAL PARTICLE STATES APPLET - P. Falstad VERY VERY EXTENSIVE. 1-Dimensional Particle States Calculator (Schrödinger Calculator) is "...a quantum mechanics simulation that shows the behavior of a single particle in bound states in one dimension. It solves the Schrödinger equation and allows you to visualize the solutions..." For more information see Math, Physics & Engineering Applets or Paul Falstad's Home Page CLASSICAL WAVEPACKET SOLUTION TO SCHRÖDINGER'S EQUATION - C.W.P. Palmer & J. Paulin, Department of Physics, University of Oxford VERY EXTENSIVE. For more information see How does Quantum Mechanics turn into Classical or the Department of Physics SOLUTIONS TO THE SCHRÖDINGER EQUATION - William Benfold, University of Southampton, U.K. VERY EXTENSIVE. Solutions to the Schrödinger Equation Calculator "...illustrates the use of a "Shooting Method" to find solutions to the Schrödinger equation, with various different types of potential function. The default is "square wells", where the potential V(x) is constant, save for finitely many square wells..." For more information see Applets or Benfold TIME DEPENDENT SCHRÖDINGER EQUATION (JAVA APPLET) - C. Cecka, Institute for Computational and Mathematical Engineering (iCME), Stanford University VERY EXTENSIVE. For more information see Cris Cecka's Home Page or the Institute for Computational and Mathematical Engineering (iCME) THE TIME-DEPENDENT SCHRÖDINGER EQUATION - William Benfold, University of Southampton, U.K. VERY EXTENSIVE. The Time-Dependent Schrödinger Equation Calculator "...shows the evolution over time of a gaussian wave function, with either a series of potential wells, or a quadratic potential. As usual, the depth, width and number of wells may be varied using the text fields provided. In addition, the initial width, position and energy of the the wave function can be chosen. The potential will be marked on the graph, either as a quadratic curve, or as pairs of vertical markers (edges of potential wells)...." For more information see Applets or Benfold VISUAL SCHRÖDINGER: A VISUALIZER-SOLVER APPLET FOR THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION (JAVA APPLET) - K. Schmidt, Department of Physics and Astronomy, Arizona State University & M.A. Lee, Department of Physics, Kent State University VERY VERY EXTENSIVE. Visual Schrödinger Calculator "...numerically solves the one-dimensional Schrödinger equation for a variety of standard Hamiltonians and permits users to define their own potential functions and rapidly display the results..." Some prepared examples of the Schrödinger Calculator include the: "...1-D Harmonic Oscillator; L=1, Radial 3-d Harmonic Oscillator; H Atom 1s State and H Atom 2p State; Cl 2 Morse Potential; Malfliet-Tjon Deuteron; 30th Excited of 0.5*x**4; The Double Harmonic Oscillator; Square Well; Two Narrow Pulses; "Atom" for Solid Slab and Solid Slab; Infinite Well Super Symmetric Partner..." For more information see Kevin Schmidt's Home Page HAMILTONIAN CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS THE SPIN-BOSON HAMILTONIAN (JAVA APPLET) - J. Gea-Banacloche, Department of Physics, University of Arkansas VERY EXTENSIVE. Spin-Boson Hamiltonian Calculator "...features a quantized harmonic oscillator coupled to a two-level system. The parameters in (1) are referred to, in the text Fields below, as the "spin frequency", "oscillator frequency" and "coupling"..." For more information see Julio Gea-Banacloche's Home-Made Page NUMERICAL HAMILTONIAN PROBLEMS (JAVA APPLET) - S.A. Sarra, Department of Mathematics, Marshall University VERY VERY EXTENSIVE. Numerical Hamiltonian Problems Calculator "...demonstrates the integration of six model Hamiltonian systems by a variety of sympletic and non-sympletic methods..." For more information see Scott A. Sarra's Home Page or the Department of Mathematics HEISENBERG CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS HEISENBERG'S UNCERTAINTY PRINCIPLE CALCULATORS & APPLETS HEISENBERG'S UNCERTAINTY PRINCIPLE (JAVA APPLET) - W.S. Warren, Department of Chemistry, Princeton University Heisenberg's Uncertainty Principle Calculator "...illustrates one version of the Heisenberg Uncertainty Principle, which relates uncertainties in certain pairs of measurable quantities..." For more information see Chemistry 215 FERMI CALCULATORS & APPLETS FERMI SURFACE DATABASE CALCULATORS, APPLETS, ANNIMATIIONS, SIMULATIONS FERMI SURFACE DATABASE (APPLETS, JPEG, VRML1 & VRML2) - S. Hershfield, C.J. Stanton, Tat-Sang (Alex) Choy, J. Naset & J. Chen, Department of Physics, College of Liberal Arts and Sciences, University of Florida Multimedia Fermi Surface Database (Text, Images, Animations, Simulations, etc.). VERY VERY EXTENSIVE. For more information see Selman Hershfield's Home Page; Christopher J. Stanton's Home Page or the Department of Physics Other Fermi Surface Databases include Fermi Surfaces in Stereo3D and Java3D Periodic Table of the Fermi Surfaces of Elemental Solids FERMI SURFACES - Jörg Bergmann, Institut für Theoretische Physik, TU Dresden, Germany Multimedia Fermi Surfaces Database (Text, Images, Animations, Simulations, etc.). VERY VERY EXTENSIVE. Fermi Surfaces "...Fermi surfaces, Fermi velocities and character of the electronic states at the Fermi surfaces are visualised based on ab initio electronic structure calculations within a scalar-relativistic or fully relativistic optimized LCAO scheme for the light and heavy elements, respectively..." "...The velocity at the Fermi surface is indicated by continuously changing colours from low velocity states (blue) to high velocity states (red)..." For more information see Jörg Bergmann's Home Page or the Institut für Theoretische Physik ATOMIC QUANTUM MECHANIC CALCULATORS & APPLETS ATOMIC QUANTUM MECHANICS APPLET - SooHaeng Yoo, E.J. Walter, N.J. Ramer & A.M. Rappe, The Rappe Group, Theoretical Physical Chemistry, Department of Chemistry, University of Pennsylvania VERY VERY VERY...EXTENSIVE. Atomic Quantum Mechanics Calculator: "...Pick an atom and its electronic configuration and see the wavefunctions calculated right before your eyes...uses Density Functional Theory to compute all of the ground-state wavefunctions for any element on the periodic table..." For more information see the Atomic Quantum Mechanics: Visualizing the Wave Function; Java; Education; The Rappe Group; Theory, Simulation, and Modeling; Chemical Physics and Physical Chemistry or the Department of Chemistry COHERENT STATES OF QUANTUM HARMONIC OSCILLATOR - GLAUBER STATES COHERENT STATES OF QUANTUM HARMONIC OSCILLATOR (JAVA APPLET) - Author: O. Psencik and modified by L. Kocbach, Atomic Physics, Theoretical Physics Section, Department of Physics, University of Bergen, Norway VERY EXTENSIVE. Coherent States of Quantum Harmonic Oscillator Calculator "...these states of harmonic oscillator, so called coherent states, are known as Glauber states, and they are known as single harmonic oscillator prototypes of the coherent states of oscillating electromagnetic field, which are the model of ideal continuous wave laser field, or an electromagnetic field of unmodulated radio wave..." For more information see Atomic Physics Courses & Demonstrations; Ladislav Kocbach's Home Page or Atomic Physics

HILBERT CURVES CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS, SIERPINSKI CURVES CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS PEANO CURVES CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS HILBERT, SIERPINSKI AND PEANO SPACE-FILLING CURVES APPLET - V.B. Balayoghan, Department of Computer Science, University of Texas, Austin, Texas VERY EXTENSIVE. Hilbert, Sierpinksi & Peano Space-Filling Curves Calculator "...draws the sequences of curves that define the 2-dimensional Hilbert, Sierpinski and Peano space-filling curves and several of their variations..." Hilbert, Sierpinksi & Peano Space-Filling Curves Calculator INPUT Values include: Select Curve "...Hilbert; Moore; Sierpinski; Sierpinski_C; Sierpinski_R; Peano; Peano_S; Peano_R; or Peano_M..." Select Recursive Level (1 thru 8)..." For more information see A Motley Assemblage of Stuff - Java Applets; V.B. Balayoghan's Home Page or the Department of Computer Science KRONIG-PENNEY MODEL CALCULATORS & APPLETS KRONIG-PENNEY MODEL (JAVA APPLET) - K. Schmidt, Department of Physics and Astronomy, Arizona State University VERY EXTENSIVE. For more information see Old PHY577 Quantum Mechanics web page or Kevin Schmidt's Home Page KRONIG-PENNEY MODEL (JAVA APPLET) - William Benfold, University of Southampton, U.K. VERY EXTENSIVE. Kronig-Penny Model Calculator "...displays the energy-momentum diagrams produced by the Kronig-Penney model for periodic potential..." For more information see Applets or Benfold QUANTUM MONTY HALL CALCULATORS & APPLETS QUANTUM MONTY HALL (JAVA APPLET) - M. Key, Institut für Mathematische Physik, Fachbereich Physik, Technische Universität Braunschweig, Deutschland (Germany) The Monty Hall Problem "...is a well-known problem in statistics, which time and again leads to controversies because of its counter-intuitive solution. Here we consider a quantum version, which illustrates nicely some differences between classical and quantum information..." Quantum Monty Hall Calculator "...simulates directly the stages of the Quantum Monty Hall Problem. It runs in a loop of three frames..." For more information see The Quantum Monty Hall Problem; Michael Key's Home Page; Quanten-Informatik in Braunschweig or the Institut für Mathematische Physik QUANTUM INTERFERENCE CALCULATORS & APPLETS METROLOGY WITH QUANTUM INTERFERENCE (JAVA APPLET) - N.Ph. Georgiades, E.S. Polzik & H.J. Kimble, Quantum Optics Group, Norman Bridge Laboratory of Physics, California Institute of Technology, (CIT) VERY VERY EXTENSIVE. Metrology with Quantum Interference "...Quantum interference in the rate of two-photon excitation of the 6S1/2 -->6P3/2 -->6D5/2 transition in atomic cesium is exploited to demonstrate phase-sensitive frequency demodulation for an optical interval of +/- 12.5 THz..." For more information see Quantum Interference and Frequency Metrology or the Quantum Optics Group RIPPLE TANK SIMULATION (JAVA APPLET) - P. Falstad VERY VERY EXTENSIVE. Ripple Tank Calculator "...demonstrates waves in two dimensions, including such wave phenomena as interference, diffraction (single slit, double slit, etc.), refraction, resonance, phased arrays, and the Doppler effect..." For more information see Math, Physics & Engineering Applets or Paul Falstad's Home Page TWO-PHOTON QUNATUM INTERFERENCE CALCULATOR (JAVA APPLET) - N.Ph. Georgiades, E.S. Polzik & H.J. Kimble, Quantum Optics Group, Norman Bridge Laboratory of Physics, California Institute of Technology, (CIT) VERY EXTENSIVE. Two-Photon Quantum Interference Calculator (Quantum Interference Calculator) "...allows the user to change several parameters of the problem and calculate characteristics of the resulting Quantum Interference..." For more information see Quantum Interference and Frequency Metrology or the Quantum Optics Group QUANTUM BARRIER PENETRATION CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS QUANTUM TUNNELING CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS QUANTUM TUNNELING (SHOCKWAVE) - Vladimir Gavryushin, Functional combinations in solid states, Department of Semiconductor Physics, Vilnius University, Lithuania Quantum Tunneling Calculator "...allows the user to choose a potential energy barrier of a standard shape (square, triangular, or trapezoidal) or to create a potential barrier of arbitrary shape..." For more information see Quantum Mechanics QUANTUM TUNNELING - Physics Education Technology, Department of Physics, College of Arts & Sciences, University of Colorado Quantum Tunneling Calculator "...Watch quantum "particles" tunnel through barriers. Explore the properties of the wave functions that describe these particles..." For more information see Quantum Phenomena Simulations; Physics Simulations; Physics Education Technology or the Department of Physics

Quantum Computation

Handbook of Quantum Information for Undergraduates, Graduates & Scientists Undergraduate Quantum Computation, Qubits, Quantum Information Courses & Lectures Graduate Quantum Computation, Quantum Information Courses & Lectures Quantum Computer Calculators & Simulations Quantum Circuit Calculators & Simulations Teleportation Calculators & Applets Quantum Cryptography Courses, Lectures, etc. (Mathematics Calculators Center)

Quantum Computation HANDBOOK OF QUANTUM INFORMATION Handbook of Quantum Information For Undergraduates, Graduates & Scientists HANDBOOK OF QUANTUM INFORMATION - Quantiki & Qubit.org, Center for Quantum Computation, Universities of Oxford and Cambridge, U.K. Multimedia Handbook of Quantum Information: Quantum Teaching Modules (Text & Images). VERY VERY VERY...EXTENSIVE. Examples from the "Handbook of Quantum Information" Sections & Subsections include: Mathematical Structure "...Hilbert spaces; Bra-ket notation; Density matrix; Tensor products; Observables and measurements; Operators; etc..." Quantum States "...Qubits and Qudits; Pure States; Ensembles; States with well known properties..." Evolution and Operations "...Unitarity and time evolution; Measurements and preparations; State transformations criteria (majorization); etc..." Entanglement "...Bell's theorem; Entanglement measures; Entanglement of particular states; Multipartite entanglement; etc..." Quantum Information Theory "...Classical information; Quantum information; Quantum state compression; etc..." Quantum Communication; Quantum Cryptography; Quantum Computation; Quantum Algorithms; etc. For more information see Quantiki; Center for Quantum Computation or Qubit.org UNDERGRADUATE: QUBITS, QUANTUM MECHANICS, QUANTUM COMPUTATION, QUANTUM INFORMATION COURSES Undergraduate Courses & Lectures QUANTUM COMPUTATION: PHYSICS 219/COMPUTER SCIENCE 219 - J. Preskill, Theoretical Physics, Division of Physics, Mathematics, and Astronomy, and the Institute for Quantum Information, California Institute of Technology Multimedia Quantum Computation Course (Text & Images). VERY VERY VERY...EXTENSIVE. Quantum Computation Chapters include: "...Foundations of Quantum Theory I: States and Ensembles; Foundations of Quantum Theory II: Measurement and Evolution; Quantum Entanglement; Quantum Information Theory; Quantum Computation; Quantum Error Correction; etc..." For more information see John Preskill's Home Page or the Institute for Quantum Information QUANTUM COMPUTATION - U. Vazirani, Computer Science Division, Department of Electrical Engineering and Computer Sciences, College of Engineering, University of California, Berkeley Multimedia Quantum Computation Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples from over "26" Quantum Computation Lectures include "...Hilbert Space, Tensor product, Quantum gates, Bell states, Inequalities, etc.; Reversibility, Quantum Computers are Digital; Quantum Complexity Theory; Simon's Agorithm + QFT; Quantum Factoring; Lower Bounds for Unstructured Search, Quantum Zeno Effect; Quantum Information; Quantum Lower Bounds - Guest Lecture by Robert Spalek; Holevo's Theorem, Random Access Codes; Adiabatic Quantum Computation; Stabilizer Formalism; etc..." For more information see Umesh Vazirani's Home Page or the Computer Science Division QUANTUM COMPUTATION - N. David Mermin, Laboratory of Atomic & Solid Physics, Department of Physics, College of Arts and Sciences, Cornell University Multimedia Quantum Computation Course - PDF, 170+ Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of Quantum Computation Lectures include "...Chapter 1: Fundamental Properties of Cbits and Qbits; Chapter 3: Breaking RSA Encryption with a Quantum Computer: Shor’s Factoring Algorithm; Chapter 5: Quantum Error Correction; etc..." For more information see N. David Mermin's Home Page or the Department of Physics QUANTUM COURSES - Center for Quantum Computation, Oxford University, U.K. Multimedia Quantum Courses (Text & Images). VERY VERY VERY...EXTENSIVE. Quantum Courses include Introduction to Quantum Computation Course includes "...Quantum Logic Gates; Quantum Networks; Quantum Entanglement; Decoherence; Selected Quantum Algorithms; Elements of Computational Complexity; Quantum Error Correction; Fault Tolerant Quantum Computation; etc..." Control of Quantum Systems Course includes "...Why Quantum Control; Control System Models; Open-loop, Closed-loop and Learning Approaches to Control; Controllability and Control System Identification..." For more information see the Center for Quantum Computation or Qubit.org QUBITS, QUANTUM MECHANICS AND COMPUTERS (C/CS/PHYS191) - M. Crommie & U. Vazirani, Computer Science Division, Department of Electrical Engineering and Computer Sciences, College of Engineering, University of California, Berkeley Multimedia Qubits, Quantum Mechanics & Computers Course (Text & Images). VERY VERY VERY...EXTENSIVE. Qubits, Quantum Mechanics & Computers Subject Categories include: "...Qubits, Measurements; Bell States, Bell Inequalities; Hilbert Spaces, Tensor Products; Photon Polarization - Photon Qubits; Quantum Factoring Algorithm; Quantum Teleportation Experiments; etc..." For more information see Umesh Vazirani's Home Page; EECS Courses or the EECS Instructional & Electronics Support or the Department of Electrical Engineering and Computer Sciences Undergraduate Teaching Modules INTRODUCTION TO ENTANGLEMENT THEORY - Quantum Information in Braunschweig, Institut für Mathematische Physik, Technische Universität Braunschweig, Germany Multimedia Introduction to Entanglement Theory Course (Text & Images). VERY EXTENSIVE. Entanglement "...is a physical ressource. It is for example the key ingredient for a quantum computer, allowing to solve certain tasks better and more quickly. But it is an NP hard problem to decide whether a given state is entangled or not..." For more information see Quanten-Informatik in Braunschweig; Quanten-Informatik in Braunschweig or the Institut für Mathematische Physik

GRADUATE: QUBITS, QUANTUM MECHANICS, QUANTUM COMPUTATION, QUANTUM INFORMATION, ETC. COURSES Graduate Courses & Lectures with Videos/Movies & Sound QUANTUM COMPUTATION LECTURES (WINDOWS MEDIA PLAYER) - David Deutsch, Centre for Quantum Computation, Clarendon Laboratory, Oxford University, U.K. Multimedia Quantum Computation Lectures (Text, Images, Videos/Movies & Audio/Sound). VERY VERY VERY...EXTENSIVE. Quantum Computation Lectures include: The Qubit "...Introducing quantum theory, the quantum theory of computation, physical systems, observations, and the simplest quantum physical system, the qubit..." Interference "...Performing and analysing a single-photon interference experiment..." Measurement "...How to analyse pairs of interacting quantum systems..." The Schroedinger Picture "...Introducing the Schroedinger Picture, density matrices, state vectors, pure states and the Schroedinger equation..." A Quantum Algorithm "...The Deutsch Algorithm and how it works..." Grover's Search Algorithm "...How to use quantum computation to search through N possibilities in a time proportional to the square root of N..." For more information see Lectures on Quantum Computation; David Deutsch's Home Pages; Centre for Quantum Computation, Oxford University or Quibit QUANTUM ERROR CORRECTION (FLASH & WINDOWS MEDIA PLAYER) - Daniel Gottesman, Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada Multimedia Quantum Error Correction Course (Text, Images, Videos/Movies & Audio/Sound). VERY VERY VERY...EXTENSIVE. Examples of Quantum Error Correction Lectures include "...Lecture 1: Administrative introduction, quantum operations, examples of quantum channels, etc; Lecture 3: Finite field GF(4), stabilizer codes as GF(4) codes, perfect quantum codes, definition of Clifford group, etc; Lecture 5: Generators of symplectic group, quantum Gilbert-Varshamov bound, quantum Hamming bound, etc.; Lecture 9: Circuit assumptions for fault tolerance re-examined (other universal gate sets, local gates, fresh ancillas, etc; etc..." For more information see Daniel Gottesman's Home Page or the Perimeter Institute for Theoretical Physics QUANTUM COMPUTER CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS JQUANTUM - QUANTUM COMPUTER SIMULATION (JAVA APPLET) - Andreas de Vries, jQuantum, Fachbereich Technische Betriebswirtschaft, Germany VERY VERY EXTENSIVE. Quantum Computer Calculator "...simulates a quantum computer. You can design quantum circuits with it and let them run. The current state of the quantum register is illustrated..." For more information see jQuantum or Fachbereich Technische Betriebswirtschaft QUANTUM COMPUTER SIMULATION (JAVA APPLETS) - J.A. Vaccaro, Senior Lecturer, Centre for Quantum Dynamics, School of Science, Faculty of Science, Griffith University, Nathan, Queensland, Australia Multimedia Interactive Simulations with Tutorials (Text, Images & Simulations). VERY VERY EXTENSIVE. Quantum Computer Simulation "...demonstrates the basic principles on which quantum computers are based: superposition and interference. The superposition principle allows may operations to occur simultaneously..." For more information see John A. Vaccaro's Home Page; Centre for Quantum Dynamics or Griffith University QUANTUM COMPUTATION APPLET - J. Wasserman, Department of Physics & Astronomy, Johns Hopkins University VERY VERY EXTENSIVE. Quantum Computation Applet "...demonstrates some of the basic concepts of quantum computation. Quantum information theory makes use of qubits, or Quantum Bits. Qubits,..." Quantum Computation Calculator INPUT Values include: Select One of the Following "...PauliX; PauliY; PauliZ; Hadamard; Phase (S) or Pi/8 (T)..." Viewing Angle "...Alpha 296; Beta 178; Gamma 153..." Quibit Theta 0; Phi 0; Phase 0; Qubit Theta 180; Phi 0; Phase 0; etc. For more information see Virtual Quantum Mechanics or the Department of Physics & Astronomy QUANTUM CIRCUIT CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS QUASI - QUANTUM CIRCUIT SIMULATOR (JAVA APPLET) - M. Eck & P. Wocjan, Institut für Algorithmen und Kognitive Systems (IAKS), Fakultät für Informatik, Uinversität Karlsruhe, Germany VERY VERY EXTENSIVE. Quantum Circuit Simulator "...is able to build and simulate quantum circuits in a graphical user interface..." For more information see QuaSi's Home Page or the Institut für Algorithmen und Kognitive Systems (IAKS) TELEPORTATION CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS TELEPORTATION APPLET - Takashi Yamanoue, Kagoshima University, Japan In English & Japanese Teleportation Applet: "...is constructed by the user (you) at the object editor, on the upper part of the applet. The object is made of cubical parts. If the teleportation button is clicked, the information of the object is sent to the virtual factory(receiver) on the lower part of the applet. The identical object is constructed..."

Relativity & Tensors GENERAL RELATIVITY & DIFFERENTIAL GEOMETRY COURSES & LECTURES INTRODUCTION TO DIFFERENTIAL GEOMETRY AND GENERAL RELATIVITY - S. Waner, Department of Mathematics, Hofstra University Multimedia Differential Geometry and General Relativity Course (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of Differential Geometry and General Relativity Course Chapters include "...Smooth Manifolds and Scalar Fields; Contravariant and Covariant Vector Fields; Riemannian Manifolds Covariant Differentiation; Geodesics and Local Inertial Frames; The Riemann Curvature Tensor; The Stress Tensor and the Relativistic Stress-Energy Tensor; Three Basic Premises of General Relativity; etc..." For more information see Online Utilities & Software - Calculators; Finite Mathematics & Applied Calculus Resource Page; Steven R. Costenoble's Home Page; Department of Mathematics or Hofstra University GENERAL RELATIVITY LECTURE NOTES - Matthias Blau, Gravity and String Theory Group, Institut de Physique, Université de Neuchâtel, Switzerland Multimedia General Relativity Course Lecture Notes - PDF - 229 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. General Relativity Lecture Notes Chapters include "...The Physics and Geometry of Geodesics; Tensor Algebra; Physics in a Gravitational Field; The Lie Derivative, Symmetries and Killing Vectors; The Schwarzschild Metric; Particle and Photon Orbits in the Schwarzschild Geometry; Linearised Gravity and Gravitational Waves; Kaluza-Klein Theory; etc..." For more information see Matthias Blau's Lecture Notes; Matthias Blau's Home Page; Gravity and String Theory Group or the Institut de Physique DIFFERENTIAL GEOMETRY - Matt Visser, Gravity Group, Mathematics, School of Mathematics, Statistics and Computer Science, Victoria University of Wellington, New Zealand Multimedia Differential Geometry Notes - PDF - 224 Pages (Text & Images). VERY VERY VERY...EXTENSIVE. Examples of Differential Geometry Chapters & Subchapters include Chapter 2: Fundamentals "...Basis and sub-basis for a topology; Discrete and indiscrete topologies; Hausdorff and non-Hausdorff topologies; Elementary metric spaces; etc..." Chapter 3: Affine Connexions "...Parallel transport; Geodesics; Torsion; Basic Curvature Identities; Weitzenbock connexion; etc..." Chapter 6: Metric tensor "...Riemannian geometry; Finsler/pseudo-Finsler geometry; The Weyl tensor; etc..." Chapter 8: Lie derivatives "...Lie derivatives on covariant vectors; Lie derivatives on general tensors; etc..." For more information see Lecture Notes; Math 464: Differential Geometry; Teaching; Matt Visser's Home Page or the School of Mathematics, Statistics and Computer Science RELATIVITY CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS THE RELATIVITY CALCULATOR - J.T. Mitchell, PHENIX Experimental Group, Relativistic Heavy Ion Collider (RHIC), Brookhaven National Laboratory (BNL) VERY EXTENSIVE. Relativity Calculator "...calculates physical properties at relativistic speeds. You input the speed of the object, its mass, length, and clock time, and the calculator will automatically calculate what the object will look like to you..." For more information see Relativistic; Jeffery Mitchell's RHIClets; Jeffery Thomas Mitchell's Home Page; PHENIX Software Page; PHENIX Experimental Group; Relativistic Heavy Ion Collider (RHIC) or the Brookhaven National Laboratory (BNL) RELATIVITY APPLET - T. Tao, Department of Mathematics, UCLA VERY VERY EXTENSIVE. Relativity Calculator Options include: "...An Inertial Reference Frame; An Inertial Object of Zero Length; A Non-inertial Object of Zero Length; A Inertial Object of Non-zero Length; A Light Ray or An Event..." For more information see Applets; Terence Tao's Home Page or the Department of Mathematics VLSR CALCULATOR: CALCULATE THE VELOCITY OF THE LOCAL STANDARD OF REST - E.M. Murphy, The Far Spectroscopic Explorer (FUSE), Department of Physics and Astronomy, Johns Hopkins University & NASA VLSR Calculator: Calculate the Velocity of the Local Standard of Rest "...will calculate the radial velocity of the observer with respect to a given RA and DEC on the date of observation for a number of popular standards of rest..." For more information see FUSE Planning Tools or The Far Spectroscopic Explorer (FUSE) RELATIVISTIC ACCELERATION CALCULATORS & APPLETS - TIME DILATION CONSTANT PROPER-ACCELERATION CALCULATOR - P. Fraundorf, Department of Physics & Astronomy, University of Missouri, St. Louis VERY VERY EXTENSIVE. Constant Proper-Acceleration Calculator "...provides students with quantitative tools for dealing with time dilation, relativistic acceleration, and even curved space-time..." For more information see One-Frame Views of Unidirectional Motion; Phil Fraundorf's Home Page or the Department of Physics & Astronomy

GENERAL RELATIVITY TEACHING MODULES, CALCULATORS, APPLETS & ANIMATIONS SPECIAL RELATIVITY TEACHING MODULES, CALCULATORS, APPLETS & ANIMATIONS AN ILLUMINATING INTRODUCTION TO RELATIVITY: THE LIGHT CONE - R. Salgado, Department of Physics, Syracuse University Multimedia Relativity Teaching Modules (Text, Images, Simulations & Applets). For more information see Interactive Simulations; Physics Courses or the Department of Physics GENERAL RELATIVIEY & SPECIAL RELATIVITY - C.R. Nave, Department of Physics & Astronomy, College of Arts & Sciences, Georgia State University VERY VERY EXTENSIVE. Multimedia General Relativity & Special Relativity Course (Text, Images, Simulations & Calculators). For more information see HyperPhysics; Carl Rod Nave's Home Page; Department of Physics & Astronomy or Georgia State University SPECIAL RELATIVITY (JAVA APPLET) - Physics 1, Department of Physics, California Institute of Technology (CIT) VERY EXTENSIVE. Special Relativity Calcaultor "...demonstrates some physical effects of Einstein's Special Relativity..." Special Relativity Calculator Options include: "...Experiment 1: Perpendicular Rods; Experiment 2: Flying Clocks; Experiment 3: A Light Clock; Experiment 4: Moving Michelson-Morley; Experiment 5: Barn & Ladder Paradox; Experiment 6: Car Headlight Experiment;..." For more information see Physics 1 Applet Page or Physics 1b (Analytical): Special Relativity and Electromagnetism SPECIAL RELATIVITY - A. Hamilton, Center for Astrophysics and Space Astronomy (CASA) Department of Astrophysical and Planetary Sciences, University of Colorado Multimedia Special Relativity Course (Text, Images, Animations & Videos/Movies). VERY VERY VERY...EXTENSIVE. For more information see Andrew Hamilton's Home Page or the Center for Astrophysics and Space Astronomy Some examples from over "8" Special Relativity Chapters & Videos/Movies include Chapter 1: The Postulates of Special Relativity Chapter 3: Centre of the Lightcone Chapter 5: Time Dilation Chapter 6: Construction of the Lorentz Transformation

TENSOR CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS TENSOR COMPONENTS ON CURVED SPACETIMES CALCULATORS & APPLETS GRTENSOR II DEMONSTRATIONS - P. Musgrave, Astronomy Research Group, Department of Physics, Queen's University, Kingston, Ontario, Canada VERY VERY VERY...EXTENSIVE. GRTensorII "...a computer algebra package for performing calculations in the general area of differential geometry. Its purpose is the calculation of tensor components on curved spacetimes specified in terms of a metric or set of basis vectors..." Demonstrations of GRTensorII currently available are in the areas of: "...General Relativity & Geometry; Black Hole Perturbations; The GRJunction Package & Engineering Applications.." For more information see GRTensor II or the Department of Physics TENSORS & RELATIVITY - Peter Dunsby, Department of Mathematics and Applied Mathematics, University of Cape Town, South Africa VERY VERY VERY...EXTENSIVE. Multimedia Tensors & Relativity Course (Text, Images, Animations & Simulations). For more information see Online Courses or the Department of Mathematics and Applied Mathematics Some examples from over "8" Tensors & Relativity Chapters include The Special Theory of Relativity Tensors in Special Relativity Einstein's Field Equations Scattering, Absorption & Extinction SCATTERING, ABSORPTION & EXTINCTION RELATED CENTERS FOR SCATTERING, ABSORPTION & EXTINCTION DATABASES SEE PHYSICS DATABASES SCATTERING, ABSORPTION AND EXTINCTION EFFIEIENCIES CALCULATORS & APPLETS MIECALC: FREELY CONFIGURABLE PROGRAM FOR LIGHT SCATTERING CALCULATIONS (MIE THEORY) (JAVA APPLET) - B. Michel, Scientific Consulting, Bundesrepublik Deutschland (Germany) VERY VERY EXTENSIVE. MieCalc Calculator Calculates "...optical cross-sections, efficiencies, angular scattering properties as functions of freely selectable parameters..." MieCalc Calculator INPUT Values include: "...Refractive Index of the Medium (refmed); Imaginary Part of the Refractive Index of the Particle (refim); Wavelength in Vacuum (lambda); Diameter of the Particle (d); etc..." For more information see Optics Online or Bernhard Michel - Light scattering, Analysis of Optical Systems

Sensors & Devices SENSORS & DEVICES RELATED CENTERS FOR RELATED CALCULATORS & APPLETS SEE THE ELECTRICAL & COMPUTER ENGINEERING CALCULATORS CENTER SENSOR CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS TEMPERATURE CONTROL CALCULATORS & APPLETS TEMPERATURE CONTROL/REGELUNG (JAVA APPLETS) - R. Moros, Institut für Technische Chemie, Universität Leipzig VERY VERY EXTENSIVE. Temperature Control Applets include: "...Charakterisierung der Regelstrecke; Berechnung der Reglerparameter; Test der Regelung..." For more information see Institut für Technische Chemie, Universität Leipzig TEMPERATURE SENSOR CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS IEC 751 PRT UTILITY - Isotech, U.K. EC 751 PRT Calculator INPUT Values include: "...Convert Resistance to Temperature Calculator; Coefficients; Calculate Custom Probe Coefficients; Select Ro or Rwtp..." For more information see Isotech RTD CALCULATOR (RESISTANCE TEMPERATURE DETECTORS CALCULATOR) - Capgo Pty Ltd Resistance Temperature Detectors (RTDs) "...rely on the predictable and repeatable phenomena of the electrical resistance of metals changing with temperature..." Resistance Temperature Detector Calculator INPUT Values include: "...Resistance Temperature Detector (RTD) Resistance; Resistance Temperature Detector (RTD) Resistance at 0 Degrees C.; Resistance Temperature Detector (RTD) Type; Temperature Units; Temperature..." For more information see Introduction to RTDs; Temperature; Online Resources or Capgo SENSOR CALC - Minco Products, Inc. VERY VERY EXTENSIVE. Sensor Calculator "...Online table generator for RTD's, thermocouples, and temperature sensitive heaters..." Sensor Calculators include: RTD Calculator: "...Calculate temperature and resistance tables for Minco's RTD Elements..." Heater Calculator: "...Calculate temperature and resistance tables for Minco's wire-wound..." Thermocouple Calculator: "...Calculate temperature and milivolt tables for Thermocouples based on..." For more information see Engineering Tools or Minco Products THERMISTOR CALCULATOR (JAVA APPLET) - Capgo Pty Ltd VERY EXTENSIVE. Thermistor Calculator INPUT Values include: "...Temperature Unit; Temperature; Calibration Points or Thermistors Constants; Resistance;..." For more information see Thermistor Temperature Sensors; Introduction to Temperature Measurement; Temperature; Online Resources or Capgo THERMOCOUPLE CALCULATOR (JAVA APPLET) - Capgo Pty Ltd VERY EXTENSIVE. Thermocouple Calculator "...will compute the temperature to 0.1° C given the reference junction temperature, the measured thermocouple voltage and the thermocouple type..." For more information see Temperature; Online Resources or Capgo ZERO BALANCE CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS ZERO BALANCE CALCULATOR - Futek Advanced Sensor Technology, Inc. Zero Balance Calculator "...is used to determine the value of a resistor that, when places in parallel with the bridge, will balance the sensor's zero..." Zero Balance Calculator INPUT Values include: "...Bridge Resistance; Excitation; Zero Value..." For more information see Calculators or Futek Advanced Sensor Technology, Inc. Examples of other Sensor Calculators include Shunt Calibration Calculator Shunt Calibration Calculator INPUT Values include: "...Bridge Resistance; Desired Output..." Span Adjustment Calculator Span Adjustment Calculator INPUT Values include: "...Actual Output; Desired Output; Resistance (Excitation Leg)..." Spectroscopy SPECTROSCOPY RELATED CENTERS FOR MORE SPECTROSCOPY COURSES, LECTURES, CALCULATORS, DATABASES, ETC. SEE THE CHEMISTRY CALCULATORS CENTER: SPECTROSCOPY EXAMPLES OF SPECTROSCOPY DATABASE, CALCULATORS & APPLETS MOLECULAR SPECTRAL DATABASE: DIATOMIC, TRIATOMIC & HYDROCARBON SPECTRAL DATABASES - National Institute of Standards and Technology (NIST) Multimedia Molecular Spectral Databases (Text & Images). VERY VERY VERY...EXTENSIVE. Molecular Spectral Databases include the "...Diatomic Spectral Database; Triatomic Spectral Database & the Hydrocarbon Spectral Database..." "...Each of the databases covers primarily the microwave region with some data available for the radio frequency region..." "...Rotational spectral lines for 121 diatomic molecules, 55 triatomic molecules, and 91 hydrocarbon molecules have been tabulated. The isotopic molecular species, assigned quantum numbers, observed frequency, estimated measurement uncertainty, and reference are given..." For more information see the NIST Physics Laboratory Physical Reference Data or the National Institute of Standards and Technology (NIST) X-RAY PHOTOELECTRON SPECTROSCOPY (XPS) DATABASE - C.D. Wagner, A.V. Naumkin, A. Kraut-Vass, J.W. Allison, C.J. Powell, J.R. Rumble Jr., National Institute of Standards and Technology (NIST) Multimedia NIST X-ray Photoelectron Spectroscopy Database (Text & Images). VERY VERY VERY...EXTENSIVE. NIST X-ray Photoelectron Spectroscopy Database "...contains over 22,000 line positions, chemical shifts, doublet splittings, and energy separations of photoelectron and Auger-electron lines..." For more information see NIST Standard Reference Data Web Server; NIST Online Scientific Databases or the National Institute of Standards and Technology (NIST) VIRTUAL SPECTROMETER - VIRSPEC (JAVA APPLET) - A. Zheludev, Neutron Scattering Group, Solid State Division, Oak Ridge National Laboratory (ORNL) VERY VERY EXTENSIVE. Spectrometer Calculator is "...a Java-based 3-axis spectrometer simulator/resolution calculator/false peak calculator...It calculates angles and simulates scans. It also calculates several type of false peaks. As the virtual spectrometer is moved, a Ben Sternlieb- style graphical resolution window is updated in real time, showing the resolution parameters and ellipses at current position..." For more information see Andrey Zheludev's Home Page or the Neutron Scattering Group SPECTROSCOPY TOOLS: 1H-WIZZARD (CHEMICAL SHIFTS): IR-WIZZARD (WAVE NUMBER); MS-WIZZARD (FRAGMENT OR LOSS MASS); ETC.. - Institut für Chemie, Universität Potsdamm, Bundesrepublik Deutschland (Germany) VERY VERY VERY...EXTENSIVE. Spectroscopy Courses include: "...Applications of 1H NMR Spectroscopy..." Spectroscopy Calculators include: "...1H-Wizard; IR-Wizard; MS-Wizard; Enhanced IR-Wizard (more than 2000 entries)..." Spectroscopy Databases & Calculators include: 1H chemical shifts; 15N chemical shifts; 31P chemical shifts; NMR- Solvents; J(H,H)- Couplings; 13C chemical shifts Calculator; 17O chemical shifts; 13C chemical shift; etc..." For more information see Spectroscopic Tools or the Institut für Chemie

Sports Physics SPORTS RELATED CENTERS FOR MORE SPORTS RELATED CALCULATORS & APPLETS SEE SPORTS CALCULATORS SPORTS PHYSICS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS AUTO RACING CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS PHYSICS OF RACING - Authors: B. Beckman & R. Keller Multimedia Physics of Auto Racing Course (Text & Images). Examples from over "23" Physics of Racing Teaching Modules include: "...Weight Transfer; Keeping Your Tires Stuck to the Ground; Basic Calculations; There Is No Such Thing as Centrifugal Force; Introduction to the Racing Line; Speed and Horsepower; The Traction Budget; Simulating Car Dynamics with a Computer Program; Straights; etc..." For more information see Robert Keller's Home Page THE PHYSICS OF MOTORSPORT - R.G. Brower, Department of Physics, University of Durham, U.K. Multimedia Physics of Motorsport Course (Text & Images). Physics of Motorsport Course "...looks at the physics involved in designing and driving fast racing cars. It will concentrate mainly on four wheeled, petrol driven vehicles, but the same physical problems apply to all kinds of vehicles..." Physics of Motorsport Teaching Modules Subject Categories include: "...Power or Torque?; The Straights; The Racing Line; Skids and Why they Happen; etc..." For more information see Physics of Motorsport Homepage; Richard Bower's Personal Home Page; Richard Bower's Home Page at the Department of Physicsor the Department of Physics SPORTS PHYSICS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS BASEBALL CALCULATORS, SIMULATIONS, VIDEOS/MOVIES & AUDIO/SOUND BASEBALL COURSES, TEACHING MODULES, LECTURES PHYSICS AND ACOUSTICS OF BASEBALL & SOFTBALL BATS (QUICKTIME) - D.A. Russell, Applied Physics, Department of Science & Mathematics, Kettering University, Flint, Michigan Multimedia Physics and Acoustics of Baseball and Softball Bats Teaching Modules (Text, Images, Animations & Videos/Movies). VERY VERY VERY...EXTENSIVE. Physics and Acoustics of Baseball and Softball Bats "...There is a tremendous amount of physics and engineering that goes into the design of a baseball or softball bat, especially the new high-tech aluminum and composite bats which are currently dominating the market. There is also an amazing amount of physics involved in the bat-ball collision, and in the performance and behavior of the bat itself..." Physics and Acoustics of Baseball and Softball Bats Teaching Modules include: "...What happens when ball meets bat?; How large are the forces between bat and ball?; How does bat weight affect swing speed and ball velocity?; Which matters more: total weight or mass distribution (inertia)?; What is the COP (center of percussion) and does it matter?; What (and where) is the sweet spot of a bat?; etc..." For more information see Acoustics & Vibrations; Daniel A. Russell's Home Page; Applied Physics; Department of Science & Mathematics or Kettering University THE PHYSICS OF BASEBALL (WINDOWS MEDIA PLAYER) - A.M. Nathan, Department of Physics, College of Engineering, University of Illinois, Urbana-Champaign Multimedia Physics of Baseball Courses, Teaching Modules & Lectures (Text, Images, Videos/Movies & Audio/Sound). VERY VERY VERY...EXTENSIVE. The Physics of Baseball Courses, Teaching Modules & Lectures include "...The Physics of Baseball; The Effect of Spin on the Flight of a Baseball; The Physics of the Trampoline Effect in Baseball and Softball Bats; How to Hit Home Runs: Optimum Baseball Bat Swing Parameters for Maximum Range Trajectories; Paradoxical popups: Why are they hard to catch?; Newton in the Batter's Box; Baseball at High Altitude; etc..." For more information see Alan M. Nathan's Home Page; Nuclear Physics Laboratory or the Department of Physics BASEBALL PITCH SIMULATION (JAVA APPLET) - M. van Rooij & H. Higuchi, Department of Mechanical and Aerospace Engineering, L.C. Smith College of Engineering and Computer Science, Syracuse University Multimedia Baseball Pitch Simulation (Text & Images). VERY EXTENSIVE. Baseball Pitch Calculator INPUT Values inlcude: "...Velocity; Rotational Speed; Position Angle Theta; Position Angle Phi; Launch Angle Theta; Launch Angle Beta..." For more information see Baseball; Sports Aerodynamics; Fluid Dynamics Calculators; Fluid Dynamics Home Page; Hiroshi Higuchi's Home Page or the Department of Mechanical and Aerospace Engineering HOW DOES THE SPINNING OF THE BALL AFFECT THE FLOW? (JAVA APPLET) - M. van Rooij & H. Higuchi, Department of Mechanical and Aerospace Engineering, L.C. Smith College of Engineering and Computer Science, Syracuse University For more information see Sports Aerodynamics; Fluid Dynamics Calculators; Fluid Dynamics Home Page; Hiroshi Higuchi's Home Page or the Department of Mechanical and Aerospace Engineering CURVEBALL: EXPERT VERSION - Glenn Research Center, NASA VERY VERY VERY...VEXTENSIVE. CurveBall: Expert Version "...The expert version includes the effects of aerodynamic drag and weight on the flight of the ball. The resulting flight path is three dimensional, so you must specify some additional parameters not found on the student version. You can also view the results of the pitch from behind home plate..." For more information see Aeronautics; Beginner's Guide to Aeronautics; Glenn Learning Technologies Project or the Glenn Research Center Other Baseball Calculators & Simulations include CurveBall: Student Version CurveBall: Student Version "...With this software you can investigate how a big league pitcher throws a curveball by changing the values of the factors that affect the aerodynamic forces on the ball..." Ideal Lift of a Spinning Ball Calculator Ideal Lift of a Spinning Ball Calculator "...All that is necessary to create lift is to turn a flow of air. The airfoil of a wing turns a flow, and so does a rotating cylinder. A spinning ball also turns a flow and generates an aerodynamic lift force. The details of how a spinning ball creates lift are fairly complex. Next to any surface, the molecules of the air stick to the surface, as discussed in the properties of air slide. This thin layer of molecules entrains or pulls the..." Curveball Trajectory Calculator Curveball Trajectory Calculator "...As the force acts on the ball, it is deflected along its flight path. If we neglect the viscous forces on the ball, which slow it down and change the magnitude and direction of the force, we have a constant force always acting perpendicular (at a right angle) to the flow direction..."

SPORTS PHYSICS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS FOOTBALL PHYSICS SIMULATIONS, VIDEOS/MOVIES & AUDIO SOUND FOOTBALL PHYSICS (QUICKTIME) - T.J. Gay, THE Gay Group, Department of Physics & Astronomy, University of Nebraska Multimedia Football Physics Course (Text, Images, Videos/Movies & Audio/Sound). VERY VERY VERY...EXTENSIVE. Football Physics "...basic physics concepts that play an important role in the game of football..." Examples from over "18" Football Physics Video Lectures include: "...Inertia Video Lecture; Vectors Video Lecture; Newton's Third Law Video Lecture; Impulse Video Lecture; Atoms and Photons Video Lecture; Quickness, Speed, Power and Strength Video Lecture; Momentum Video Lecture; Punting Video Lecture; Symmetry Video Lecture; Distribution of Force Video Lecture; Energy Consumption Video Lecture; Tackling Video Lecture; Kinematics Video Lecture; Advanced Momentum Video Lecture; Turf Physics Video Lecture; etc..." For more information see The Gay Group Home Page or the Department of Physics & Astronomy SPORTS PHYSICS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS GOLF CALCULATORS & APPLETS GOLF BALL TRAJECTORY SIMULATION (JAVA APPLET) - M. van Rooij & H. Higuchi, Department of Mechanical and Aerospace Engineering, L.C. Smith College of Engineering and Computer Science, Syracuse University Multimedia Golf Ball Trajectory Simulation (Text & Images). VERY EXTENSIVE. Golf Ball Trajectory Calculator "...A golf ball is strongly influenced by aerodynamic forces. Golfers discovered that the golf ball flew farther when it had dimples. These "conventional" golf balls have either 330 or 336 round dimples placed in regular rows. A "hexagonally" dimpled ball, which has 290 "hexagonal" dimples and 12 "pertagonal" dimples, will fly even farther..." Golf Ball Trajectory Calculator INPUT Values include: "...Surface (Smooth; Hexagonal Dimpled Ball); Launch Velocity; Rotationa Speed; Lanuch Angle..." For more information see Golf Ball; Sports Aerodynamics; Fluid Dynamics Calculators; Fluid Dynamics Home Page; Hiroshi Higuchi's Home Page or the Department of Mechanical and Aerospace Engineering SPORTS PHYSICS CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS ROWING CALCULATORS, APPLETS, ANIMATIONS & SIMULATIONS PHYSICS OF ROWING - A.