Chapter 1 A review of the origins of quantum theory

1.1 ...and there was light!

1.2 The quantization of energy

1.3 Particle/wave duality

1.4 The two-slit diffraction experiment

1.5 Uncertainty and indeterminacy

1.6 Non-classical phenomena

References

Problems

Chapter 2 The state of a quantum system

2.1 The classical description of the state of a particle

2.2 The wave function for a single particle

2.3 Measurements on a quantum system

2.4 The wave function for a free particle

2.5 Free particle beams and scattering experiments

References

Problems

Chapter 3 The representation of dynamical variables

3.1 Eigenvalue equations

3.2 Energy eigenstates

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

3.4 Scattering by a one-dimensional potential step

3.5 Scattering by a one-dimensional square well

References

Problems

Chapter 4 More about dynamical variables

4.1 Compatible and incompatible variables

4.2 The angular momentum operators

4.3 The radial momentum operator

4.4 The parity operator

4.5 Orbital angular momentum eigenfunctions and eigenvalues

4.6 Angular distributions in orbital angular momentum eigenstates

4.7 Rotational energy levels in nuclei and molecules

References

Problems

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

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

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

5.3 Vibrational spectra of molecules and nuclei

5.4 Thermal oscillations,phonons and photons

References

Problems

Chapter 6 Ladder operators:angular momentum

6.1 The ladder operator method for the angular momentum spectrum

6.2 Electron spin

6.3 Addition of angular momenta

References

Problems

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

7.1 Three-dimensional systems with spherical symmetry

7.2 The hydrogen atom

7.3 Atomic structure

7.4 Periodic potentials and translational symmetry

7.5 Energy bands

7.6 Crystalline solids

References

Problems

Chapter 8 Magnetic effects in quantum systems

8.1 The Hamiltonian for a charged particle in an electromagnetic field

8.2 The effects of applied magnetic fields on atoms

8.3 The Stern-Gerlach experiment and electron spin

8.4 Spin-orbit coupling

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

8.6 Periodic effects in two-dimensional conductors

8.7 The quantum Hall effect

References

Problems

Chapter 9 The superposition principle

9.1 The prediction of the results of experiments on quantum systems

9.2 The superposition expansion

9.3 Expectation values and uncertainties

9.4 Superpositions of momentum eigenfunctions

9.5 Position eigenstates and the Dirac delta function

References

Problems

Chapter 10 The matrix formulation of quantum mechanics

10.1 Alternatives to Schr？dinger's wave mechanics

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

10.3 The matrix representation for dynamical variables

10.4 Eigenvalue equations in the matrix formulation

10.5 A spin-half particle in a magnetic field

10.6 The Dirac notation

References

Problems

Chapter 11 Approximate methods for solving the Schr？dinger equation

11.1 Time-independent perturbation theory

11.2 First-order perturbations:a one-dimensional problem

11.3 Second-order perturbations:anharmonic oscillations

11.4 Degenerate perturbation theory:spin-orbit coupling

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

References

Problems

Chapter 12 Time-dependent problems

12.1 The time-dependent Schr？dinger equation

12.2 Resonant transitions between two energy levels

12.3 Time-dependent perturbation theory

12.4 Selection rules for electric dipole radiation spectra

12.5 Transition rates and Fermi's golden rule

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

References

Problems

Chapter 13 Many-particle systems

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

13.2 The Born-Oppenheimer approximation

13.3 Identical particles and the Pauli exclusion principle

13.4 Systems containing two identical particles

References

Problems

Chapter 14 Coherence in quantum mechanics

14.1 Coherence in a system containing many identical particles

14.2 Successive Stern-Gerlach experiments

14.3 Two-particle correlation experiments

14.4 Determinism, locality and Bell's inequality

References

Problems

Appendix A The two-body problem in classical mechanics

A1 The kinetic energy of a two-particle system

A2 Two particles interacting through a central force

Appendix B Analytical solutions of eigenvalue equations

B1 Legendre's equation

B2 The energy eigenvalue equation for the simple harmonic oscillator

B3 The radial equation for the hydrogen atom

Appendix C The computer demonstrations

C1 The Schr？dinger equation in one dimension

C2 The Kronig-Penney model

C3 The Schr？dinger equation:central potentials

C4 Orbital angular momentum

C5 Transmission

C6 Wave packets

Index