Solid state physics grew out of applications of quantum mechanics to the problem of electron conduction in solids. This seemingly simple problem defied solution because the presence of an ion at each lattice site seemed to present an obvious impediment to conduction. How the electrons avoid the ions was thus the basic question. Although the answer to this question is well known, it does serve to illuminate the very essence of solid state physics: there is organization in the many. Each electron adjusts its wavelength to take advantage of the periodicity of the lattice. In the absence of impurities, conduction is perfect. Hence, by understanding this simple fact that periodicity implies perfect conduction, it became clear that the experimentally observed resistivity in a metal came not from electrons running into each of the ions but rather from dirt (disorder), thermal effects mediated by dynamical motion of the ions, or electron–electron interactions. This book examines each of these effects with an eye for identifying underlying organizing principles that simplify the physics of such interactions.

Spontaneously broken symmetry

The search for organizing principles that help simplify the physics of many-body systems is at the heart of modern solid state or, more generally, condensed matter physics. One such tool is symmetry. Consider the simple case of permutation symmetry typically taught in a first class in quantum mechanics. This symmetry was introduced into quantum mechanics by W. Heisenberg in the context of the indistinguishability of identical particles.