Quantum Methods with Mathematica®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. |
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 |
465 | |
469 | |