Quantum mechanicsPDF电子书下载

Chapter 1 A review of the origins of quantum theory 1

1.1 ...and there was light! 1

1.2 The quantization of energy 5

1.3 Particle/wave duality 10

1.4 The two-slit diffraction experiment 13

1.5 Uncertainty and indeterminacy 18

1.6 Non-classical phenomena 23

References 26

Problems 27

Chapter 2 The state of a quantum system 31

2.1 The classical description of the state of a particle 31

2.2 The wave function for a single particle 33

2.3 Measurements on a quantum system 37

2.4 The wave function for a free particle 40

2.5 Free particle beams and scattering experiments 42

References 46

Problems 46

Chapter 3 The representation of dynamical variables 49

3.1 Eigenvalue equations 49

3.2 Energy eigenstates 52

3.3 Bound states of a particle in a one-dimensional square potential well 56

3.4 Scattering by a one-dimensional potential step 64

3.5 Scattering by a one-dimensional square well 68

References 74

Problems 74

Chapter 4 More about dynamical variables 79

4.1 Compatible and incompatible variables 79

4.2 The angular momentum operators 81

4.3 The radial momentum operator 84

4.4 The parity operator 86

4.5 Orbital angular momentum eigenfunctions and eigenvalues 89

4.6 Angular distributions in orbital angular momentum eigenstates 92

4.7 Rotational energy levels in nuclei and molecules 95

References 102

Problems 103

Chapter 5 Ladder operators:the one-dimensional simple harmonic oscillator 107

5.1 The energy spectrum of a one-dimensional simple harmonic oscillator 107

5.2 The energy eigenfunctions of the one-dimensional simple harmonic oscillator 111

5.3 Vibrational spectra of molecules and nuclei 115

5.4 Thermal oscillations,phonons and photons 120

References 125

Problems 126

Chapter 6 Ladder operators:angular momentum 131

6.1 The ladder operator method for the angular momentum spectrum 131

6.2 Electron spin 135

6.3 Addition of angular momenta 137

References 143

Problems 144

Chapter 7 Symmetry and the solution of the Schr？dinger equation 147

7.1 Three-dimensional systems with spherical symmetry 147

7.2 The hydrogen atom 150

7.3 Atomic structure 156

7.4 Periodic potentials and translational symmetry 160

7.5 Energy bands 165

7.6 Crystalline solids 171

References 175

Problems 176

Chapter 8 Magnetic effects in quantum systems 183

8.1 The Hamiltonian for a charged particle in an electromagnetic field 183

8.2 The effects of applied magnetic fields on atoms 187

8.3 The Stern-Gerlach experiment and electron spin 189

8.4 Spin-orbit coupling 192

8.5 The motion of free electrons in a uniform magnetic field:Landau levels 196

8.6 Periodic effects in two-dimensional conductors 199

8.7 The quantum Hall effect 202

References 206

Problems 206

Chapter 9 The superposition principle 211

9.1 The prediction of the results of experiments on quantum systems 211

9.2 The superposition expansion 213

9.3 Expectation values and uncertainties 217

9.4 Superpositions of momentum eigenfunctions 222

9.5 Position eigenstates and the Dirac delta function 227

References 229

Problems 229

Chapter 10 The matrix formulation of quantum mechanics 235

10.1 Alternatives to Schr？dinger's wave mechanics 235

10.2 The representation of the state of a particle in a discrete basis 237

10.3 The matrix representation for dynamical variables 240

10.4 Eigenvalue equations in the matrix formulation 243

10.5 A spin-half particle in a magnetic field 246

10.6 The Dirac notation 250

References 252

Problems 252

Chapter 11 Approximate methods for solving the Schr？dinger equation 255

11.1 Time-independent perturbation theory 255

11.2 First-order perturbations:a one-dimensional problem 260

11.3 Second-order perturbations:anharmonic oscillations 263

11.4 Degenerate perturbation theory:spin-orbit coupling 265

11.5 A variational method for finding the ground state of a bound particle 270

References 274

Problems 275

Chapter 12 Time-dependent problems 281

12.1 The time-dependent Schr？dinger equation 281

12.2 Resonant transitions between two energy levels 285

12.3 Time-dependent perturbation theory 289

12.4 Selection rules for electric dipole radiation spectra 293

12.5 Transition rates and Fermi's golden rule 295

12.6 High-energy elastic scattering by a finite-range potential 298

References 302

Problems 303

Chapter 13 Many-particle systems 307

13.1 The wave function for a system of non-interacting particles 307

13.2 The Born-Oppenheimer approximation 310

13.3 Identical particles and the Pauli exclusion principle 314

13.4 Systems containing two identical particles 318

References 326

Problems 326

Chapter 14 Coherence in quantum mechanics 329

14.1 Coherence in a system containing many identical particles 329

14.2 Successive Stern-Gerlach experiments 332

14.3 Two-particle correlation experiments 337

14.4 Determinism, locality and Bell's inequality 342

References 346

Problems 346

Appendix A The two-body problem in classical mechanics 349

A1 The kinetic energy of a two-particle system 349

A2 Two particles interacting through a central force 351

Appendix B Analytical solutions of eigenvalue equations 353

B1 Legendre's equation 353

B2 The energy eigenvalue equation for the simple harmonic oscillator 356

B3 The radial equation for the hydrogen atom 358

Appendix C The computer demonstrations 361

C1 The Schr？dinger equation in one dimension 362

C2 The Kronig-Penney model 365

C3 The Schr？dinger equation:central potentials 365

C4 Orbital angular momentum 366

C5 Transmission 366

C6 Wave packets 367

Index 369