Introduction to quantum mechanics, by Robert H. Dicke and James P. Wittke

An introduction to the physical concepts and mathematical formations of nonrelativistic quantum mechanics designed as a textbook for courses at the graduate level but also suitable for advanced undergraduates. By limiting the scope of the text to the nonrelativistic theory, the authors are able to explore the basic concepts of quantum mechanics carefully while avoiding both the complications and unsatisfactory aspects of field theory. A knowledge of calculus and some familiarity with differential equations is assumed, as well as knowledge of basic undergraduate-level physics, including classical mechanics. The opening chapters suggest how the basic concepts of classical mechanics must be altered to explain many atomic-scale phenomena and lay the groundwork for the more formal, postulational approach to quantum mechanics which follows. The concluding part represents a considerable broadening of the viewpoint and of the scope of the problems that can be handled. Of special importance is the final chapter, dealing with quantum-statistical mechanics, wherein techniques that are playing an ever-increasing role in modern physics re developed. Throughout the text, emphasis is given to algebraic techniques and their power and elegance are clearly shown. CHAPTER 1. INTRODUCTION 1 1-1 Quantum mechanics, a system of dynamics 1 1-2 Evidence of the inadequacy of classical mechanics 3 1-3 Some necessary characteristics of quantum theory 14 1-4 Summary 18 CHAPTER 2. WAVE MECHANICS 21 2-1 The wave-particle duality 21 2-2 The wave function 23 2-3 The uncertainty relation 27 2-4 Wave packets 31 2-5 Summary . 34 CHAPTER 3. SCHRODINGER'S EQUATION 36 3-1 The equation of motion of a wave function 36 3-2 One-dimensional motion past a potential hill 40 3-3 One-dimensional motion: reflection by an infinitely wide barrier 46 3-4 One-dimensional motion in a potential well 50 3-5 Particle flux 60 3-6 Summary 62 CHAPTER 4. FOURIER TECHNIQUES AND EXPECTATION VALUES . 64 4-1 The Fourier integral 64 4-2 The Kronecker delta and the Dirac delta function 66 4-3 Eigenvalue equations 69 4-4 Expectation values 71 4-5 Summary 75 CHAPTER 5. REVIEW OF CLASSICAL MECHANICS 77 5-l Introduction 77 5-2 Generalized coordinates and Lagrange's equations 77 5-3 Hamilton's equations 82 5-4 Poisson brackets 85 5-5 Canonical transformations 86 5-6 Summary . 88 CHAPTER 6. OPERATOR FORMALISM 90 6-1 Postulates of quantum mechanics. 90 6-2 Algebraic methods 103 6-3 Many-particle systems 109 6-4 Summary 112 CHAPTER 7. MEASUREMENT 115 7-1 The meaning of measurement 115 7-2 Photon polarization 116 7-3 Summary 121 CHAPTER 8. THE CORRESPONDENCE PRINCIPLE 122 8-1 The relation of quantum mechanics to classical mechanics 122 8-2 The transition from quantum mechanics to classical mechanics 122 8-3 The correspondence principle and the uncertainty relation. 129 8-4 The minimum uncertainty wave function 131 8-5 The uncertainty principle and the simple harmonic oscillator . 132 8-6 Summary 134 CHAPTER 9. ANGULAR MOMENTUM 137 9-1 Orbital angular-momentum operators 137 9-2 Orbital angular-momentum wave functions 142 9-3 Angular momentum in general 148 9-4 Addition of angular momenta 149 9-5 Class T operators 1 52 9-6 Summary . 1 54 CHAPTER 10. CENTRAL FORCES 1 56 1 0-1 Qualitative behavior with an attractive potential 1 56 1 0-2 The hydrogenic atom 158 1 0-3 The three-dimensional oscillator 166 1 0-4 The free particle 170 1 0-5 Parity 172 10-6 Summary. 174 CHAPTER 1 1 . MATRIX REPRESENTATIONS 176 1 1 -1 Matrix representations of wave functions and operators 176 1 1-2 Matrix algebra . 177 1 1-3 Types of matrix representation 180 1 1-4 Infinite matrices . 184 1 1-5 Summary . 186 CHAPTER 12. SPIN ANGULAR MOMENTUM 189 12-1 Matrix representation of angular-momentum operators 189 12-2 Systems with spin one-half 194 12-3 Electron-spin precession 195 12-4 Paramagnetic resonance 199 12-5 Summary . 205 CHAPTER 13. TRANSFORMATIONS OF REPRESENTATIONS 208 13-1 Introduction . 208 13-2 A geometrical analogue-Hilbert space 210 13-3 Eigenvalue equations 212 13-4 Group properties of unitary transformations 214 13-5 Continuous matrices. 214 13-6 Canonical transformations 217 13-7 Summary . 222 CHAPTER 14. APPROXIMATION METHODS. 226 14-1 The need for approximation methods 226 14-2 Time-independent perturbation theory 226 14-3 Time-dependent perturbation theory 237 14-4 Variational techniques 242 14-5 The WKB method . 245 14-6 Summary . 253 CHAPTER 15. INTERACTION WITH A STRONG ELECTROMAGNETIC FIELD. 259 15–1 The Hamiltonian of a particle in an electromagnetic field 259 15–2 Motion of a free electron in a uniform magnetic field 260 15–3 The weak-field Zeeman effect . 265 15-4 The g-factor . 269 15–5 The strong-field Zeeman effect 270 15–6 Interaction of an atomic electron with a plane electromagnetic wave . 272 15–7 Selection rules 278 15–8 Summary . 282 CHAPTER 16. SCATTERING 285 16-1 Physical concepts 285 16-2 The Born approximation 291 16-3 Partial waves 297 16-4 Summary . 308 CHAPTER 17. IDENTICAL PARTICLES 311 17-1 The particle-exchange operator 311 17-2 The Pauli principle . 312 17-3 The spin-independent Hamiltonian 315 17-4 Effect of spin symmetry on the energy of a state 318 17-5 Valence binding in the hydrogen molecule 324 17-6 Para- and ortho-hydrogen . 327 17-7 Systems of more than two particles 329 17-8 Summary . 329 CHAPTER 18. QUANTUM-STATISTICAL MECHANICS 331 18-1 Introduction . 331 18-2 The density matrix . 332 18-3 The equation of motion of the density matrix 337 18-4 Ordered and disordered ensembles 338 18-5 Stationary ensembles 342 18-6 Systems of noninteracting particles 345 18-7 Ideal gas . 349 18-8 Summary . 354 TABLE OF ATOMIC CONSTANTS . 360 INDEX . 361