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Overview
Topics include the dual nature of matter and radiation, state functions and their interpretation, linear momentum, the motion of a free particle, Schrödinger's equation, approximation methods, angular momentum, and many other subjects. In the interests of keeping the mathematics as simple as possible, most of the book is confined to considerations of one-dimensional systems. A selection of 150 problems, many of which require prolonged study, amplify the text's teachings and an appendix contains solutions to 50 representative problems. This edition also includes a new Introduction by Joseph A. Rudnick and Robert Finkelstein.
Product Details
| ISBN-13: | 9780486485966 |
|---|---|
| Publisher: | Dover Publications |
| Publication date: | 03/14/2012 |
| Series: | Dover Books on Physics Series |
| Edition description: | Unabridged |
| Pages: | 446 |
| Product dimensions: | 6.10(w) x 9.20(h) x 1.00(d) |
About the Author
David S. Saxon (1920–2005) was a longtime physics professor and administrator at UCLA. He was a leader in the UCLA administration from 1967 to 1975 and head of the University of California system from 1975 to 1983.
Table of Contents
I The Dual Nature of Matter and Radiation
1 The breakdown of classical physics 1
2 Quantum mechanical concepts 3
3 The wave aspects of particles 5
4 Numerical magnitudes and the quantum domain 12
5 The particle aspects of waves 13
6 Complementarity 16
7 The correspondence principle 16
II State Functions and Their Interpretation
1 The idea of a state function; superposition of states 18
2 Expectation values 23
3 Comparison between the classical and quantum descriptions of a state; wave packets 25
III Linear Momentum
1 State functions corresponding to a definite momentum 29
2 Construction of wave packets by superposition 31
3 Fourier transforms; the Dirac delta function 34
4 Momentum and configuration space 38
5 The momentum and position operators 39
6 Commutation relations 45
7 The uncertainty principle 47
IV Motion of a Free Particle
1 Motion of a wave packet; group velocity 56
2 The correspondence principle requirement 59
3 Propagation of a free particle wave packet in configuration space 60
4 Propagation of a free particle wave packet in momentum space; the energy operator 62
5 Time development of a Gaussian wave packet 64
6 The free particle Schrödinger equation 66
7 Conservation of probability 68
8 Dirac bracket notation 72
9 Stationary states 73
10 A particle in a box 75
11 Summary 81
V SchröDinger's Equation
1 The requirement of conservation of probability 84
2 Hermitian operators 85
3 The correspondence principle requirement 91
4 Schrödinger's equation in configuration and momentum space 95
5 Stationary states 97
6 Eigenfunctions and eigenvalues of Hermitian operators 101
7 Simultaneous observables and complete sets of operators 104
8 The uncertainty principle 106
*9 Wave packets and their motion 111
10 Summary: The postulates of quantum mechanics 111
VI States of a Particle in One Dimension
1 General features 117
2 Classification by symmetry; the parity operator 119
3 Bound states in a square well 121
4 The harmonic oscillator 127
*5 The creation operator representation 139
*6 Motion of a wave packet in the harmonic oscillator potential 145
7 Continuum states in a square well potential 147
8 Continuum states in general; the probability flux 153
*9 Passage of a wave packet through a potential 155
*10 Numerical solution of Schrödinger's equation 159
VII Approximation Methods
1 The WKB approximation 175
2 The Rayleigh-Ritz approximation ]85
3 Stationary state perturbation theory 189
4 Matrices 201
5 Degenerate or close-lying states 205
6 Time dependent perturbation theory 209
VIII Systems of Particles in One Dimension
1 Formulation 227
2 Two particles: Center-of-mass coordinates 229
3 Interacting particles in the presence of uniform external forces 233
*4 Coupled harmonic oscillators 237
5 Weakly interacting particles in the presence of general external forces 239
6 Identical particles and exchange degeneracy 241
7 Systems of two identical particles 243
8 Many-particle systems; symmetrization and the Pauli exclusion principle 245
*9 Systems of three identical particles 249
10 Weakly interacting identical particles in the presence of general external forces 255
IX Motion in Three Dimensions
1 Formulation: Motion of a free particle 263
*2 Potentials separable in rectangular coordinates 265
3 Central potentials; angular momentum states 269
4 Some examples 279
5 The hydrogenic atom 287
X Angular Momentum and Spin
1 Orbital angular momentum operators and commutation relations 299
2 Angular momentum eigenfunctions and eigenvalues 303
*3 Rotation and translation operators 313
4 Spin: The Pauli operators 317
*5 Addition of angular momentum 327
XI Some Applications and Further Generalizations
*1 The helium atom; the periodic table 345
*2 Theory of scattering 351
*3 Green's function for scattering; the Born approximation 361
*4 Motion in an electromagnetic field 373
*5 Dirac theory of the electron 377
*6 Mixed states and the density matrix 387
Appendices
I Evaluation of integrals containing Gaussian functions 397
II Selected references 401
III Answers and solutions to selected problems 403
*For a one-semester course, any or all of the starred sections can be omitted without harm to the logical development (see Preface).