# Book:A.P. French/An Introduction to Quantum Physics

## A.P. French and Edwin F. Taylor: An Introduction to Quantum Physics

Published $\text {1978}$, Nelson Thornes

ISBN 0-7487-4078-3.

Not to be referred to, you naughty students, as French and Saunders.

### Contents

PREFACE
LEARNING AIDS FOR QUANTUM PHYSICS
1 Simple models of the atom
1-1 Introduction
1-2 The classical atom
1-3 The electrical structure of matter
1-4 The Thomson atom
1-5 Line spectra
1-6 Photons
1-7 The Rutherford-Bohr atom
1-8 Further predictions of the Bohr model
1-9 Direct evidence of discrete energy levels
1-10 X-ray spectra
1-11 A note on x-ray spectroscopy
1-12 Concluding remarks
EXERCISES
2 The wave properties of particles
2-1 De Broglie's hypothesis
2-2 De Broglie above and particle velocities
2-3 Calculated magnitudes of De Broglie wavelengths
2-4 The Davisson-Germer experiments
2-5 More about the Davisson-Germer experiments
2-6 Further manifestations of the Lazarus properties of electrons
2-7 Wave properties of neutral atoms and molecules
2-8 Wave properties of nuclear particles
2-9 The meaning of the wave-particle duality
2-10 The coexistence of wave and particle properties
2-11 A first discussion of quantum amplitudes
EXERCISES
3 Wave-particle duality and bound states
3-1 Preliminary remarks
3-2 The approach to a particle-wave equation
3-3 The Schrödinger equation
3-4 Stationary states
3-3 Particle in a one-dimensional box
3-6 Unique energy without unique momentum
3-7 Interpretation of the quantum amplitudes for bound states
3-8 Particles in nonrigid boxes
3-9 Square well of finite depth
3-10 Normalisation of the wave function
3-11 Qualitative plots of bound-state wave functions
EXERCISES
4 Solutions of Schrödinger's equation in one dimension
4-1 Introduction
4-2 The square well
4-3 The harmonic oscillator
4-4 Vibrational energies of diatomic molecules
4-5 Computer solutions of the Schrödinger equation
EXERCISES
5 Further applications of Schrödinger's equation
5-1 Introduction
5-2 The three-dimensional Schrödinger equation
5-3 Eigenfunctions and eigenvalues
5-4 Particle in a three-dimensional box
5-5 Spherically symmetric solutions for hydrogen-like systems
5-6 Normalization and probability densities
5-7 Expectation values
5-8 Computer solutions for spherically symmetric hydrogen wave functions
EXERCISES
6 Photons and quantum states
6-1 Introduction
6-2 States oflinear polarization
6-3 Linearly polarized photons
6-4 Probability and the behavior of polarized photons
6-5 States of circular polarization
6-6 Orthogonality and completeness
6-7 Quantum states
6-8 Statistical and classical properties of light
6-9 Concluding remarks
APPENDIX: POLARIZED LIGHT AND ITS PRODUCTION
6A-1 The production of linearly polarized light
6A-2 The production of circularly polarized light
Suggested experiments with linearly polarized light
EXERCISES
7 Quantum amplitudes and state vectors
7-1 Introduction
7-2 The analyzer loop
7-3 Paradox of the recombined beams
7-4 Interference effect in general
7-5 Formalism of projection amplitudes
7-6 Properties of projection amplitudes
7-7 Projection amplitudes for states of circular polarization
7-8 The state vector
7-9 The state vector and the Schrödinger wave function for bound states
EXERCISES
8 The time dependence of quantum states
8-1 Introduction
8-2 Superposition of states
8-3 An example of motion in a box
8-4 Packet states in a square-well potential
8-5 The position-momentum uncertainty relation
8-6 The uncertainty principle and ground-state energies
8-7 Free-particle packet states
8-8 Packet states for moving particles
8-9 Examples of moving packet states
8-10 The energy-time uncertainty relation
8-11 Examples of the energy-time uncertainty relation
8-12 The shape and width of energy levels
EXERCISES
9 Particle scattering and barrier penetration
9-1 Scattering processes in terms of wave packets
9-2 Time-independent approach to scattering phenomena
9-3 Probability density and probability current
9-4 Scattering by a one-dimensional well
9-5 Barrier penetration: tunneling
9-6 Probability current and barrier penetration problems
9-7 An approximation for barrier penetration calculations
9-8 Field emission of electrons
9-9 Spherically symmetric probability currents
9-10 Quantitative theory of alpha decay
9-11 Scattering of wave packets
EXERCISES
10 Angular momentum
10-1 Introduction
10-2 Stern-Gerlach experiment: theory
10-3 Stern-Gerlach experiment: descriptive
10-4 Magnitudes of atomic dipole moments
10-5 Orbital angular momentum operators
10-6 Eigenvalues of $L_z$
10-7 Simultaneous eigenvalues
10-8 Quantum states of a two-dimensional harmonic oscillator
EXERCISES
11 Angular momentum of atomic systems
11-1 Introduction
11-2 Total orbital angular momentum in central fields
11-3 Rotational states of molecules
11-4 Spin angular momentum
11-5 Spin orbit coupling energy
11-6 Formalism for total angular momentum
APPENDIX: THE SCHRÖDINGER EQUATION IN SPHERICAL COORDINATES
EXERCISES
12 Ouantum states of three-dimensional systems
12-1 Introduction
12-2 The Coulomb model
12-3 General features of the radial wave functions for hydrogen
12-4 Exact radial wave functions for hydrogen
12-5 Complete Coulomb wave functions
12-6 Classification of energy eigenstates in hydrogen
12-7 Spectroscopic notation
12-8 Fine structure of hydrogen energy levels
12-9 Isotopic fine structure: heavy hydrogen
12-10 Other hydrogen-like systems
EXERCISES
13 Identical particles and atomic structure
13-1 Introduction
13-2 Schrödinger's equation for two noninteracting particles
13-3 The consequences of identity
13-4 Spin states for two particles
13-5 Exchange symmetry and the Pauli principle
13-6 When does symmetry or antisymmetry matter?
13-7 Measurability of the symmetry character
13-8 States of the helium atom
13-9 Many-electron atoms
13-10 General structure of a massive atom
EXERCISES
14-1 Introduction
14-2 The classical Hertzian dipole
14-3 Radiation from an arbitrary charge distribution
14-4 Radiating dipoles according to wave mechanics
14-5 Radiation rates and atomic Itfetimes
14-6 Selection rules and radiation patterns
14-7 Systematics of line spectra
14-8 Angular momentum of photons
14-9 Magnetic dipole radiation and galactic hydrogen
14-10 Concluding remarks
EXERCISES
BIBLIOGRAPHY