Quantum Methods with Mathematica®

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Springer Science & Business Media, 08.01.2002 - 482 Seiten

The first quantum mechanics text published that ties directly into a computer algebra system, this book exploits Mathematica(r) throughout for symbolic, numeric, and graphical computing. It is a work designed for computer interaction in an upper-division undergraduate or first-year graduate quantum mechanics course. It is also a toolbox for the practicing physicist seeking to automate a variety of algebraic and numerical tasks with the computer. The book is divided into two parts: "Systems in One Dimension" and "Quantum Dynamics." Part I emphasizes topics from a first-year course on quantum mechanics, while Part II includes more advanced topics. Although the text requires some familiarity with Mathematica, appendices are provided for gaining experience with the software and are referenced throughout the book. The text is task-oriented and integrated with numerous problems and exercises, with hints for working on the computer.

 

James M. Feagin is a Professor of Physics at California State University, Fullerton. He was educated at Georgia Tech and the University of North Carolina, Chapel Hill, where he received a Ph.D. in theoretical physics in 1980. He is a Fellow of the Alexander von Humboldt Foundation and has served as visiting Professor at the University of Freiburg, Germany. Feagin is the author of numerous articles on collision physics and the dynamics of few-body systems. He has given a number of invited talks and hosted workshops on incorporating computers into the physics curriculum and is presently helping to introduce computing into the Introductory University Physics Project (IUPP) sponsored by the American Institute of Physics.

 

Ausgewählte Seiten

Inhalt

Basic Wave Mechanics
5
11 Equations of Motion
6
12 Stationary States
9
14 TimeDevelopment Operator
10
15 Extra Dimensions
11
Particle in a Box
13
22 Numerical Eigenfunctions
16
23 Two Basic Properties
18
Potential Scattering
205
141 Numerical Solution
206
142 Scattering Amplitudes
209
143 Resonance Hunting
215
144 Radial Wavefunctions
218
145 Resonance Parameterization
220
146 Wavepacket Impact
225
Quantum Dynamics
237

24 Rectangular Wave
19
25 Quantum Rattle
24
26 Measurements
29
Uncertainty Principle
31
FreeParticle Wavepacket
35
41 Stationary Wavepacket
36
42 Moving Wavepacket
38
Parity
45
Harmonic Oscillator
51
61 Scaled Schrodinger Equation
52
62 Method of Solution
53
63 Energy Spectrum
54
64 Hermite Polynomials
58
65 Hypergeometric Functions
62
66 Normalized HO Wavefunctions
67
67 Raising and Lowering Operators
73
Variational Method and Perturbation Ideas
75
71 HO Ground State Variationally
76
72 HO Excited State Variationally
77
73 Model Hamiltonian
79
74 FirstOrder Perturbation Energy
82
Squeezed States
85
81 Eigenfunction Expansion
87
82 Time Evolution
90
83 Newtons Laws
94
84 QuasiClassical States
97
Basic Matrix Mechanics
101
91 HO Coordinate and Momentum Matrix Elements
102
92 HO Coordinate and Momentum Matrices
103
93 HO Hamiltonian Matrix
104
Partial Exact Diagonalization
107
101 ModelHamiltonian Matrix
108
102 Matrix Eigenvalues and Eigenvectors
110
103 Perturbed Eigenfunctions
113
104 Local Energy
115
105 Pseudo States and Resonances
116
Momentum Representation
121
112 Momentum Wavefunctions
124
113 Conventions
125
114 HO Momentum Wavefunctions
126
115 Dirac Delta Function
128
116 Momentum Operator
131
117 Local Energy
133
118 Coordinate Operator
134
119 MomentumSpace Hamiltonian
135
1110 Exponential Operators
136
1111 More Squeezed States
139
Lattice Representation
145
122 Momentum Lattice
150
123 Discrete Fourier Transforms
153
124 Local Energy
157
125 FFT
159
126 Wavepacket Propagation
164
127 Quantum Diffusion
180
Morse Oscillator
189
131 Kummers Equation
190
132 Eigenenergies
193
133 Eigenfunctions
195
134 Normalization
196
135 Hypergeometric Integrals
200
Quantum Operators
239
151 Commutator Algebra
240
152 TwoBody Relative Coordinates
245
153 BraKet Formalism
249
154 Harmonic Oscillator Spectrum
251
Angular Momentum
253
161 Angular Momentum Spectrum
256
162 Matrix Representation
258
163 New Axis of Quantization
261
164 Quantum Rotation Matrix
264
Angular Momentum Coupling
267
171 Spin and Orbital Coupling
271
172 Total Angular Momentum Spectrum
274
173 Clebsch Gordanary
277
174 Wigner 3j Symbols
281
175 Recoupling Coefficients
283
Coordinate and Momentum Representations
287
182 Commutation Relations
289
183 Angular Momentum in Cartesian Coordinates
292
184 Rotational Symmetry
293
185 Dynamical Symmetry
296
186 RungeLenz Vector
298
187 Hydrogen Atom Spectrum
300
Angular Momentum in Spherical Coordinates
303
191 Spherical Harmonics
308
192 New Axis of Quantization
313
193 Quantum Rotation Matrix
316
Hydrogen Atom Schrodinger Equation
323
201 Separation in Spherical Coordinates
324
202 BoundState Wavefunctions
326
203 Parity
333
204 Continuum Wavefunctions
335
205 Separation in Parabolic Coordinates
338
Wavefunctions from the RungeLenz Algebra
345
212 TopRung States
348
213 Down the Ladder
351
214 Connection with the Parabolic Separation
353
215 Linear Stark Effect
357
216 Connection with the Spherical Separation
364
Mathematica Quick View
369
Notebooks and Basic Tools
371
AII2 Projectile Motion Including Air Resistance
378
Home Improvement
383
AIII1 Functions
384
AIII2 Algebra
398
AIII3 Computing
415
Quantum Packages
423
AIV2 Quantum integExp
425
AIV4 Quantum NonCommutativeMultiply
426
AIV5 Quantum PowerTools
427
AIV6 Quantum QuantumRotations
428
AIV7 Quantum QuickRelm
430
AIV8 Quantum Trigonometry
431
Grad Div Curl
433
AV2 Cartesian Coordinates
436
AV3 Curvilinear Coordinates
445
AV4 Spherical Coordinates
448
Bibliography
465
Index
469
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