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Chapter 1 A review of the origins of quantum theory1

1.1 ...and there was light!1

1.2 The quantization of energy5

1.3 Particle/wave duality10

1.4 The two-slit diffraction experiment13

1.5 Uncertainty and indeterminacy18

1.6 Non-classical phenomena23

References26

Problems27

Chapter 2 The state of a quantum system31

2.1 The classical description of the state of a particle31

2.2 The wave function for a single particle33

2.3 Measurements on a quantum system37

2.4 The wave function for a free particle40

2.5 Free particle beams and scattering experiments42

References46

Problems46

Chapter 3 The representation of dynamical variables49

3.1 Eigenvalue equations49

3.2 Energy eigenstates52

3.3 Bound states of a particle in a one-dimensional square potential well56

3.4 Scattering by a one-dimensional potential step64

3.5 Scattering by a one-dimensional square well68

References74

Problems74

Chapter 4 More about dynamical variables79

4.1 Compatible and incompatible variables79

4.2 The angular momentum operators81

4.3 The radial momentum operator84

4.4 The parity operator86

4.5 Orbital angular momentum eigenfunctions and eigenvalues89

4.6 Angular distributions in orbital angular momentum eigenstates92

4.7 Rotational energy levels in nuclei and molecules95

References102

Problems103

Chapter 5 Ladder operators:the one-dimensional simple harmonic oscillator107

5.1 The energy spectrum of a one-dimensional simple harmonic oscillator107

5.2 The energy eigenfunctions of the one-dimensional simple harmonic oscillator111

5.3 Vibrational spectra of molecules and nuclei115

5.4 Thermal oscillations,phonons and photons120

References125

Problems126

Chapter 6 Ladder operators:angular momentum131

6.1 The ladder operator method for the angular momentum spectrum131

6.2 Electron spin135

6.3 Addition of angular momenta137

References143

Problems144

Chapter 7 Symmetry and the solution of the Schr？dinger equation147

7.1 Three-dimensional systems with spherical symmetry147

7.2 The hydrogen atom150

7.3 Atomic structure156

7.4 Periodic potentials and translational symmetry160

7.5 Energy bands165

7.6 Crystalline solids171

References175

Problems176

Chapter 8 Magnetic effects in quantum systems183

8.1 The Hamiltonian for a charged particle in an electromagnetic field183

8.2 The effects of applied magnetic fields on atoms187

8.3 The Stern-Gerlach experiment and electron spin189

8.4 Spin-orbit coupling192

8.5 The motion of free electrons in a uniform magnetic field:Landau levels196

8.6 Periodic effects in two-dimensional conductors199

8.7 The quantum Hall effect202

References206

Problems206

Chapter 9 The superposition principle211

9.1 The prediction of the results of experiments on quantum systems211

9.2 The superposition expansion213

9.3 Expectation values and uncertainties217

9.4 Superpositions of momentum eigenfunctions222

9.5 Position eigenstates and the Dirac delta function227

References229

Problems229

Chapter 10 The matrix formulation of quantum mechanics235

10.1 Alternatives to Schr？dinger's wave mechanics235

10.2 The representation of the state of a particle in a discrete basis237

10.3 The matrix representation for dynamical variables240

10.4 Eigenvalue equations in the matrix formulation243

10.5 A spin-half particle in a magnetic field246

10.6 The Dirac notation250

References252

Problems252

Chapter 11 Approximate methods for solving the Schr？dinger equation255

11.1 Time-independent perturbation theory255

11.2 First-order perturbations:a one-dimensional problem260

11.3 Second-order perturbations:anharmonic oscillations263

11.4 Degenerate perturbation theory:spin-orbit coupling265

11.5 A variational method for finding the ground state of a bound particle270

References274

Problems275

Chapter 12 Time-dependent problems281

12.1 The time-dependent Schr？dinger equation281

12.2 Resonant transitions between two energy levels285

12.3 Time-dependent perturbation theory289

12.4 Selection rules for electric dipole radiation spectra293

12.5 Transition rates and Fermi's golden rule295

12.6 High-energy elastic scattering by a finite-range potential298

References302

Problems303

Chapter 13 Many-particle systems307

13.1 The wave function for a system of non-interacting particles307

13.2 The Born-Oppenheimer approximation310

13.3 Identical particles and the Pauli exclusion principle314

13.4 Systems containing two identical particles318

References326

Problems326

Chapter 14 Coherence in quantum mechanics329

14.1 Coherence in a system containing many identical particles329

14.2 Successive Stern-Gerlach experiments332

14.3 Two-particle correlation experiments337

14.4 Determinism, locality and Bell's inequality342

References346

Problems346

Appendix A The two-body problem in classical mechanics349

A1 The kinetic energy of a two-particle system349

A2 Two particles interacting through a central force351

Appendix B Analytical solutions of eigenvalue equations353

B1 Legendre's equation353

B2 The energy eigenvalue equation for the simple harmonic oscillator356

B3 The radial equation for the hydrogen atom358

Appendix C The computer demonstrations361

C1 The Schr？dinger equation in one dimension362

C2 The Kronig-Penney model365

C3 The Schr？dinger equation:central potentials365

C4 Orbital angular momentum366

C5 Transmission366

C6 Wave packets367

Index369