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Quantum Mechanics on the Macintosh ® / by Siegmund Brandt, Hans Dieter Dahmen.

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Based on the interactive program Interquanta, Quantum Mechanics on the Macintosh, uses extensive 3-D graphics to guide the student through computer experiments in the quantum mechanics of free particle motion, bound states and scattering, tunneling, two-particle interactions, and more. It also inclu...

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Bibliographic Details
Online Access: Full Text (via Springer)
Main Author: Brandt, Siegmund
Other Authors: Dahmen, Hans Dieter
Format: eBook
Language:English
Published: New York, NY : Springer New York, 1995.
Edition:Second edition.
Subjects:
Physics.
Quantum theory.
Table of Contents:
  • 1 Introduction
  • 1.1 Interquanta
  • 1.2 The Structure of this Book
  • 1.3 The Computer Laboratory
  • 1.4 The Classroom Demonstrations
  • 1.5 Literature
  • 2 Free Particle Motion in One Dimension
  • 2.1 Physical Concepts
  • 2.2 A First Session with the Computer
  • 2.3 The Time Development of a Gaussian Wave Packet
  • 2.4 The Spectral Function of a Gaussian Wave Packet
  • 2.5 The Wave Packet as a Sum of Harmonic Waves
  • 2.6 Exercises
  • 3 Bound States in One Dimension
  • 3.1 Physical Concepts
  • 3.2 Eigenstates in the Infinitely Deep Square-Well Potential and in the Harmonic-Oscillator Potential
  • 3.3 Eigenstates in the Step Potential
  • 3.4 Harmonic Particle Motion
  • 3.5 Particle Motion in the Infinitely Deep Square-Well Potential
  • 3.6 Exercises
  • 4 Scattering in One Dimension
  • 4.1 Physical Concepts
  • 4.2 Stationary Scattering States in the Step Potential
  • 4.3 Scattering of a Harmonic Wave by the Step Potential
  • 4.4 Scattering of a Wave Packet by the Step Potential
  • 4.5 Transmission and Reflection. The Argand Diagram
  • 4.6 Exercises
  • 4.7 Analogies in Optics
  • 4.8 Reflection and Refraction of Stationary Electromagnetic Waves
  • 4.9 Reflection and Refraction of a Harmonic Light Wave
  • 4.10 Scattering of a Wave Packet of Light
  • 4.11 Transmission, Reflection and Argand Diagram for a Light Wave
  • 4.12 Exercises
  • 5 A Two-Particle System: Coupled Harmonic Oscillators
  • 5.1 Physical Concepts
  • 5.2 Stationary States
  • 5.3 Time Dependence of Global Quantities
  • 5.4 Joint Probability Densities
  • 5.5 Marginal Distributions
  • 5.6 Exercises
  • 6 Free Particle Motion in Three Dimensions
  • 6.1 Physical Concepts
  • 6.2 The 3D Harmonic Plane Wave
  • 6.3 The Plane Wave Decomposed into Spherical Waves
  • 6.4 The 3D Gaussian Wave Packet
  • 6.5 The Probability Ellipsoid
  • 6.6 Angular-Momentum Decomposition of a Wave Packet
  • 6.7 Exercises
  • 7 Bound States in Three Dimensions
  • 7.1 Physical Concepts
  • 7.2 Radial Wave Functions in Simple Potentials
  • 7.3 Radial Wave Functions in the Step Potential
  • 7.4 Probability Densities
  • 7.5 Harmonic Particle Motion
  • 7.6 Exercises
  • 8 Scattering in Three Dimensions
  • 8.1 Physical Concepts
  • 8.2 Radial Wave Functions
  • 8.3 Stationary Wave Functions and Scattered Waves
  • 8.4 Differential Cross Sections
  • 8.5 Scattering Amplitude. Phase Shift. Partial and Total Cross Sections
  • 8.6 Exercises
  • 9 Special Functions of Mathematical Physics
  • 9.1 Basic Formulae
  • 9.2 Hermite Polynomials
  • 9.3 Eigenfunctions of the One-Dimensional Harmonic Oscillator
  • 9.4 Legendre Polynomials and Associated Legendre Functions
  • 9.5 Spherical Harmonics
  • 9.6 Bessel Functions
  • 9.7 Spherical Bessel Functions
  • 9.8 Laguerre Polynomials
  • 9.9 Radial Eigenfunctions of the Harmonic Oscillator
  • 9.10 Radial Eigenfunctions of the Hydrogen Atom
  • 9.11 Simple Functions of a Complex Variable
  • 9.12 Exercises
  • 10. Additional Material and Hints for the Solution of Exercises
  • 10.1 Units and Orders of Magnitude
  • 10.2 Argand Diagrams and Unitarity for One-Dimensional Problems
  • 10.3 Hints and Answers to the Exercises
  • Appendix A.A Systematic Guide to IQ
  • A.1 Dialog Between the User and IQ
  • A.1.1 A Simple Example
  • A.1.2 The General Form of Commands
  • A.1.3 The Descriptor File
  • A.1.4 The Descriptor (Record)
  • A.1.5 The PLOT Command
  • A.1.6 The STOP Command
  • A.1.7 HELP: The Commands HE and PH
  • A.2 Coordinate Systems and Transformations
  • A.2.1 The Different Coordinate Systems
  • A.2.2 Defining the Transformations
  • A.3 The Different Types of Plot
  • A.3.1 Choosing a Plot Type: The Command CH
  • A.3.2 Cartesian 3D Plots (Type 0 Plots)
  • A.3.3 Polar 3D Plots (Type 1 Plots)
  • A.3.4 2D Plots (Type 2 Plots)
  • A.3.5 3D Column Plots (Type 3 Plots)
  • A.3.6 Special 3D Plots (Type 10 Plots)
  • A.4 The Background in the Plots
  • A.4.1 Boxes and Coordinate Axes: The Command BO
  • A.4.2 Scales
  • A.4.3 Arrows
  • A.4.4 Text and Numbers
  • A.4.5 Mathematical Symbols and Formulae
  • A.5 Further Commands
  • A.5.1 Line Styles
  • A.5.2 Multiple Plots
  • A.5.3 Combined Plots
  • A.5.4 Using Different Plotting Devices
  • A.5.5 The Different Running Modes
  • A.5.6 Introducing Physical Variables: The Commands VO toV9
  • A.5.7 Reserved Commands
  • Appendix B. How to Install IQ
  • B.1 Hardware and Operating-System Requirements
  • B.2 Diskette Format
  • B.3 Installation on a Macintosh with Hard Disk
  • B.4 Installation on a Macintosh without Hard Disk
  • B.5 Limited Memory
  • B.6 Removing Output Files
  • Appendix C. Lists of All Provided Files
  • C.1 Program File
  • C.2 Data File Specifying Graphics Devices
  • C.3 File Containing Fonts Used in Graphics
  • C.4 Descriptor Files for Examples and Exercises
  • C.5 Command Input Files and Associated Descriptor Files for Demonstrations
  • C.6 Help Files
  • Appendix D. Graphics Devices and Metafiles
  • Index of IQ Commands.

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