Interactive Quantum Mechanics

Interactive Quantum Mechanics

by Siegmund Brandt, Hans D. Dahmen, Tilo Stroh

ISBN-10: 0387002316

ISBN-13: 9780387002316

Pub. Date: 09/01/2010

Publisher: Springer-Verlag New York, LLC

At last: the new edition of Brandt and Dahmen's master piece, for years available for PC or Mac, now again available in a Java edition for Windows, Macintosh, and Linux alltogether in one book with CD-ROM. Based on the interactive program INTERQUANTA (included on the CD-ROM) and its extensive 3D color graphic features, the book guides its readers through more


At last: the new edition of Brandt and Dahmen's master piece, for years available for PC or Mac, now again available in a Java edition for Windows, Macintosh, and Linux alltogether in one book with CD-ROM. Based on the interactive program INTERQUANTA (included on the CD-ROM) and its extensive 3D color graphic features, the book guides its readers through more than 250 class-tested interactive problems.

Product Details

Springer-Verlag New York, LLC
Publication date:
Edition description:
Product dimensions:
0.75(w) x 9.21(h) x 6.14(d)

Table of Contents

1.2The Structure of This Book2
1.3The Demonstrations3
1.4The Computer Laboratory3
2Free Particle Motion in One Dimension5
2.1Physical Concepts5
2.1.1Planck's Constant. Schrodinger's Equation for a Free Particle5
2.1.2The Wave Packet. Group Velocity. Normalization6
2.1.3Probability-Current Density. Continuity Equation7
2.1.4Quantile Position. Quantile Trajectory8
2.1.5Relation to Bohm's Equation of Motion9
2.1.6Analogies in Optics10
2.2A First Session with the Computer12
2.2.1Starting IQ12
2.2.2An Automatic Demonstration12
2.2.3A First Dialog13
2.3The Free Quantum-Mechanical Gaussian Wave Packet14
2.3.1The Subpanel Physics--Comp. Coord.14
2.3.2The Subpanel Physics--Wave Packet15
2.3.3The Subpanel Physics--Quantile16
2.4The Free Optical Gaussian Wave Packet16
2.5Quantile Trajectories16
2.6The Spectral Function of a Gaussian Wave Packet18
2.7The Wave Packet as a Sum of Harmonic Waves19
3Bound States in One Dimension24
3.1Physical Concepts24
3.1.1Schrodinger's Equation with a Potential. Eigenfunctions. Eigenvalues24
3.1.2Normalization. Discrete Spectra. Orthonormality25
3.1.3The Infinitely Deep Square-Well Potential25
3.1.4The Harmonic Oscillator26
3.1.5The Step Potential26
3.1.6Time-Dependent Solutions28
3.1.7Harmonic Particle Motion. Coherent States. Squeezed States28
3.1.8Quantile Motion in the Harmonic-Oscillator Potential29
3.1.9Particle Motion in a Deep Square Well29
3.2Eigenstates in the Infinitely Deep Square-Well Potential and in the Harmonic-Oscillator Potential31
3.3Eigenstates in the Step Potential33
3.4Harmonic Particle Motion35
3.5Harmonic Oscillator: Quantile Trajectories37
3.6Particle Motion in the Infinitely Deep Square-Well Potential38
4Scattering in One Dimension45
4.1Physical Concepts45
4.1.1Stationary Scattering States. Continuum Eigenstates and Eigenvalues. Continuous Spectra45
4.1.2Time-Dependent Solutions of the Schrodinger Equation46
4.1.3Right-Moving and Left-Moving Stationary Waves of a Free Particle46
4.1.4Orthogonality and Continuum Normalization of Stationary Waves of a Free Particle. Completeness47
4.1.5Boundary Conditions for Stationary Scattering Solutions in Step Potentials48
4.1.6Stationary Scattering Solutions in Step Potentials49
4.1.7Constituent Waves50
4.1.8Normalization of Continuum Eigenstates50
4.1.9Harmonic Waves in a Step Potential50
4.1.10Time-Dependent Scattering Solutions in a Step Potential51
4.1.11Transmission and Reflection. Unitarity. The Argand Diagram52
4.1.12The Tunnel Effect53
4.1.14Phase Shifts upon Reflection at a Steep Rise or Deep Fall of the Potential54
4.1.15Transmission Resonances upon Reflection at 'More- and Less-Dense Media'56
4.1.16The Quantum-Well Device and the Quantum-Effect Device57
4.1.17Stationary States in a Linear Potential58
4.1.18Wave Packet in a Linear Potential59
4.1.19Quantile Motion in a Linear Potential59
4.2Stationary Scattering States in the Step Potential60
4.3Time-Dependent Scattering by the Step Potential61
4.4Transmission and Reflection. The Argand Diagram64
4.5Stationary Wave in a Linear Potential66
4.6Gaussian Wave Packet in a Linear Potential67
4.7Quantile Trajectories in a Linear Potential68
4.9Analogies in Optics78
4.10Reflection and Refraction of Stationary Electromagnetic Waves82
4.11Time-Dependent Scattering of Light84
4.12Transmission, Reflection, and Argand Diagram for a Light Wave86
5A Two-Particle System: Coupled Harmonic Oscillators91
5.1Physical Concepts91
5.1.1The Two-Particle System91
5.1.2Initial Condition for Distinguishable Particles93
5.1.3Time-Dependent Wave Functions and Probability Distributions for Distinguishable Particles94
5.1.4Marginal Distributions for Distinguishable Particles94
5.1.5Wave Functions for Indistinguishable Particles. Symmetrization for Bosons. Antisymmetrization for Fermions95
5.1.6Marginal Distributions of the Probability Densities of Bosons and Fermions96
5.1.7Normal Oscillations96
5.2Stationary States97
5.3Time Dependence of Global Variables98
5.4Joint Probability Densities98
5.5Marginal Distributions100
6Free Particle Motion in Three Dimensions107
6.1Physical Concepts107
6.1.1The Schrodinger Equation of a Free Particle in Three Dimensions. The Momentum Operator107
6.1.2The Wave Packet. Group Velocity. Normalization. The Probability Ellipsoid109
6.1.3Angular Momentum. Spherical Harmonics111
6.1.4The Stationary Schrodinger Equation in Polar Coordinates. Separation of Variables. Spherical Bessel Functions. Continuum Normalization. Completeness113
6.1.5Partial-Wave Decomposition of the Plane Wave114
6.1.6Partial-Wave Decomposition of the Gaussian Wave Packet114
6.2The 3D Harmonic Plane Wave117
6.3The Plane Wave Decomposed into Spherical Waves119
6.4The 3D Gaussian Wave Packet120
6.5The Probability Ellipsoid121
6.6Angular-Momentum Decomposition of a Wave Packet122
7Bound States in Three Dimensions126
7.1Physical Concepts126
7.1.1The Schrodinger Equation for a Particle under the Action of a Force. The Centrifugal Barrier. The Effective Potential126
7.1.2Bound States. Scattering States. Discrete and Continuous Spectra128
7.1.3The Infinitely Deep Square-Well Potential129
7.1.4The Spherical Step Potential130
7.1.5The Harmonic Oscillator133
7.1.6The Coulomb Potential. The Hydrogen Atom134
7.1.7Harmonic Particle Motion135
7.2Radial Wave Functions in Simple Potentials136
7.3Radial Wave Functions in the Step Potential140
7.4Probability Densities141
7.5Contour Lines of the Probability Density144
7.6Contour Surface of the Probability Density145
7.7Harmonic Particle Motion146
8Scattering in Three Dimensions152
8.1Physical Concepts152
8.1.1Radial Scattering Wave Functions152
8.1.2Boundary and Continuity Conditions. Solution of the System of Inhomogeneous Linear Equations for the Coefficients154
8.1.3Scattering of a Plane Harmonic Wave155
8.1.4Scattering Amplitude and Phase. Unitarity. The Argand Diagram159
8.1.5Coulomb Scattering160
8.2Radial Wave Functions162
8.3Stationary Wave Functions and Scattered Waves164
8.4Differential Cross Sections166
8.5Scattering Amplitude. Phase Shift. Partial and Total Cross Sections167
8.6Coulomb Scattering: Radial Wave Function170
8.7Coulomb Scattering: 3D Wave Function172
9Special Functions of Mathematical Physics179
9.1Basic Formulae179
9.1.1Hermite Polynomials179
9.1.2Harmonic-Oscillator Eigenfunctions180
9.1.3Legendre Polynomials and Legendre Functions180
9.1.4Spherical Harmonics181
9.1.5Bessel Functions182
9.1.6Spherical Bessel Functions183
9.1.7Airy Functions184
9.1.8Laguerre Polynomials185
9.1.9Radial Eigenfunctions of the Harmonic Oscillator185
9.1.10Radial Eigenfunctions of the Hydrogen Atom186
9.1.11Gaussian Distribution and Error Function186
9.1.12Binomial Distribution and Poisson Distribution187
9.2Hermite Polynomials and Related Functions188
9.3Legendre Polynomials and Related Functions189
9.4Spherical Harmonics: Surface over Cartesian Grid190
9.5Spherical Harmonics: 2D Polar Diagram191
9.6Spherical Harmonics: Polar Diagram in 3D192
9.7Bessel Functions and Related Functions193
9.8Bessel Function and Modified Bessel Function with Real Index194
9.9Airy Functions195
9.10Laguerre Polynomials195
9.11Laguerre Polynomials as Function of x and the Upper Index [alpha]197
9.12Gaussian Distribution198
9.13Error Function and Complementary Error Function199
9.14Binomial Distribution199
9.15Poisson Distribution200
9.16Simple Functions of a Complex Variable201
10Additional Material and Hints for the Solution of Exercises206
10.1Units and Orders of Magnitude206
10.1.2SI Units206
10.1.3Scaled Units207
10.1.4Atomic and Subatomic Units208
10.1.5Data-Table Units209
10.1.6Special Scales211
10.2Argand Diagrams and Unitarity for One-Dimensional Problems212
10.2.1Probability Conservation and the Unitarity of the Scattering Matrix212
10.2.2Time Reversal and the Scattering Matrix214
10.2.3Diagonalization of the Scattering Matrix215
10.2.4Argand Diagrams217
10.3Hints and Answers to the Exercises221
AA Systematic Guide to IQ248
A.1.1Starting IQ248
A.1.2Introductory Demonstration248
A.1.3Selecting a Descriptor File249
A.1.4Selecting a Descriptor and Producing a Plot249
A.1.5Printing a Plot251
A.1.6Changing Colors and Line Widths251
A.1.7Changing Parameters253
A.1.8Saving a Changed Descriptor254
A.1.9Creating a Mother Descriptor255
A.1.10Editing Descriptor Files255
A.1.11Printing a Set of Plots257
A.1.12Running a Demonstration257
A.1.14Help and Context-Sensitive Help261
A.2Coordinate Systems and Transformations261
A.2.1The Different Coordinate Systems261
A.2.2Defining the Transformations262
A.3The Different Types of Plot266
A.3.1Surface over Cartesian Grid in 3D266
A.3.2Surface over Polar Grid in 3D267
A.3.32D Function Graph269
A.3.4Contour-Line Plot in 2D271
A.3.5Contour-Surface Plot in 3D272
A.3.6Polar Diagram in 3D273
A.3.7Probability-Ellipsoid Plot275
A.3.83D Column Plot275
A.4Parameters - The Subpanel Physics276
A.4.1The Subpanel Physics--Comp. Coord.277
A.4.2The Subpanel Multiple Plot277
A.5Parameters - The Subpanel Graphics277
A.5.1The Subpanel Graphics--Geometry277
A.5.2The Subpanel Graphics--Accuracy278
A.5.3The Subpanel Graphics--Hidden Lines279
A.6The Subpanel Background280
A.6.1The Subpanel Background--Box280
A.6.2The Subpanel Background--Scales282
A.6.3The Subpanel Background--Arrows283
A.6.4The Subpanel Background--Texts285
A.7Parameters - The Subpanel Format286
A.8Coding Mathematical Symbols and Formulae286
A.9A Combined Plot and its Mother Descriptor288
A.9.1The Subpanel Type and Format288
A.9.2The Subpanel Table of Descriptors289
A.9.3Special Cases290
A.10Details of Printing290
A.10.1Preview. Colors and Line Widths290
A.10.2Using a System Printer291
A.10.3Creating PostScript Files: IQ Export292
A.11Preparing a Demonstration293
BHow to Install IQ295
B.1Contents of the CD-ROM295
B.2Computer Systems on which INTERQUANTA Can Be Used295
B.3Installation with Options. The File ReadMe.txt296
B.4Quick Installation for the Impatient User296

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