The aim of this book is to make the quantum theory of condensed matter accessible. To this end we have tried to produce a text that does not demand extensive prior knowledge of either condensed matter physics or quantum mechanics. Our hope is that both students and professional scientists will find it a user-friendly guide to some of the beautiful but subtle concepts that form the underpinning of the theory of the condensed state of matter.

The barriers to understanding these concepts are high, and so we do not try to vault them in a single leap. Instead we take a gentler path on which to reach our goal. We first introduce some of the topics from a semiclassical viewpoint before turning to the quantum-mechanical methods. When we encounter a new and unfamiliar problem to solve, we look for analogies with systems already studied. Often we are able to draw from our storehouse of techniques a familiar tool with which to cultivate the new terrain. We deal with BCS superconductivity in Chapter 7, for example, by adapting the canonical transformation that we used in studying liquid helium in Chapter 3. To find the energy of neutral collective excitations in the fractional quantum Hall effect in Chapter 10, we call on the approach used for the electron gas in the random phase approximation in Chapter 2. In studying heavy fermions in Chapter 11, we use the same technique that we found successful in treating the electron–phonon interaction in Chapter 6.