There are many good advanced books on quantum mechanics but there is a
distinct lack of books which attempt to give a serious introduction at a level
suitable for undergraduates who have a tentative understanding of mathematics, probability and classical physics.
This book introduces the most important aspects of quantum mechanics in
the simplest way possible, but challenging aspects which are essential for a
meaningful understanding have not been evaded. It is an introduction to
quantum mechanics which
. motivates the fundamental postulates of quantum mechanics by considering
the weird behaviour of quantum particles
. reviews relevant concepts in classical physics before corresponding concepts
are developed in quantum mechanics
. presents mathematical arguments in their simplest form
. provides an understanding of the power and elegance of quantum mechanics
that will make more advanced texts accessible.
Chapter 1 provides a qualitative description of the remarkable properties
of quantum particles, and these properties are used as the guidelines for a
theory of quantum mechanics which is developed in Chapters 2, 3 and 4.
Insight into this theory is gained by considering square wells and barriers in
Chapter 5 and the harmonic oscillator in Chapter 6. Many of the concepts used
in the first six chapters are clarified and developed in Chapter 7. Angular
momentum in quantum mechanics is introduced in Chapter 8, but because
angular momentum is a demanding topic, this chapter focusses on the ideas
that are needed for an understanding of the hydrogen atom in Chapter 9,
identical particles in Chapter 10 and many-electron atoms in Chapter 11.
Chapter 10 explains why identical particles are described by entangled quantum
states and how this entanglement for electrons leads to the Pauli exclusion
principle.
Chapters 7 and 10 may be omitted without significant loss of continuity.
They deal with concepts which are not needed elsewhere in the book.
I would like to express my thanks to students and colleagues at the University of Manchester. Daniel Guise helpfully calculated the energy levels in a
screened Coulomb potential. Thomas York used his impressive computing
skills to provide representations of the position probabilities for particles with
different orbital angular momentum. Sean Freeman read an early version of the
first six chapters and provided suggestions and encouragement. Finally, I
would like to thank Franz Mandl for reading an early version of the book
and for making forcefully intelligent suggestions for improvement.