Abstract

Quantum mechanics was originally developed by Schroedinger and Heisenberg as a theory of non-relativistic charged particles interacting via the Coulomb force, and successfully applied to a simple two-particle system like the hydrogen atom. However, among its most important applications has been the description of 10²³ particles found in macroscopic matter. The earliest example of this was the Sommerfeld-Bloch theory of electronic motion in metals, and its refined formulation in Landau’s Fermi liquid theory. Although solving Schroedinger’s wave equation for 10²³ interacting electrons appears an impossibly daunting task, Landau outlined a powerful strategy, involving the concept of “quasiparticles”, which allowed an essentially exact description of the low temperature properties of metals. The quasiparticles have an essentially free electron-like character. Although interactions between the electrons do strongly renormalize various parameters in the effective Hamiltonian, the quantum dynamics of the quasiparticles is essentially that of nearly free electrons, each of which can be described independently by single-particle quantum mechanics.