# ESSENTIAL QUANTUM PHYSICS

####

PETER LANDSHOFF

University of Cambridge
####

ALLEN METHERELL

University of Central Florida
####

GARETH REES

University of Cambridge

####

(Cambridge University Press)
This book provides a first course on quantum mechanics and describes simple
applications to physical phenomena that are of immediate and everyday
interest.

The first five chapters introduce the fundamentals of quantum mechanics and
are followed by a revision quiz with which readers may test their
understanding. The remaining chapters describe applications, including the
theory of spin and its application to magnetic resonance imaging, physics
of lasers, molecular binding, simple properties of crystalline solids
arising from their band structure, and the operation of junction
transistors.

Ideal either as a course text or a self-study text, the book contains
nearly 100 exercises and hints to their solution.

### Contents

#### 1 Preliminaries

Atoms; Photons; Wave nature of matter; Problems
#### 2 The Schroedinger equation

Wave functions and operators; Example: the one-dimensional
potential well; Probability interpretation and normalisation; Beams
of particles; Continuity conditions; Problems
#### 3 Special solutions

Particle in a box; The one-dimensional square well; The linear
harmonic oscillator; The tunnel effect; The delta-function
potential; The WKB approximation; Alpha decay; Problems
#### 4 The superposition principle

Linear operators; Wave packets; Ehrenfest's theorem; Hermitian
operators; Operators and observables; Commutators; Problems
#### 5 The hydrogen atom

Good quantum numbers; Orbital angular momentum; Spherically
symmetric potentials; The hydrogen atom; Many-electron atoms;
Two-body systems; The deuteron; Problems
#### Revision quiz

#### 6 The hydrogen molecule

The ionised hydrogen molecule; Other molecules; Problems.
#### 7 Introduction to perturbation theory

Time-independent perturbation theory; Time-dependent perturbation
theory; Transition probability; Energy uncertainty principle;
Sudden change in the Hamiltonian;
Example: decay of tritium; Problems
#### 8 Spin

Two kinds of angular momentum; Spin half;
The electromagnetic interaction; The Zeeman effect;
Spin precession; Problems
#### 9 Masers and lasers

Radiative transitions; Resonant absorption and stimulated emission;
Electric dipole transitions; The ammonia molecule; The ammonia maser;
Population inversion; The laser; Holography; Problems
#### 10 Band structure of crystals

Electrons in crystals; Band structure; Number of levels in a band;
Band overlap; Simple consequences of band structure; Problems
#### 11 Electron motion in crystals

Electron velocity; Motion in an external electric field; Electric
current; Effective mass and holes; Thermal excitation; Pair
excitation in intrinsic semiconductors; Problems
#### 12 Transistors

Impurities; n- and p-type semiconductors; Impurities and crystal
colour; Semiconductor junction; The diode; The junction transistor;
Two simple circuits; Problems

#### Appendices

A Power-series solutions
B The delta function and Fourier transforms
C Orbital-angular-momentum operators
D Electrodynamics
E Bloch waves
#### Hints for the problems

Click here for the first chapter of the book.