University of Cambridge

University of Central Florida

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.


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


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.