2. Many-body Quantum Mechanics

In this chapter we introduce some of the principles of many-body quantum
mechanics, applied to systems consisting of atomic nuclei and electrons.
First we outline the general principles of quantum mechanics, the properties
of wave-functions and operators, which will later be used to reformulate
the problem in terms of the density-matrix. We present the
Born-Oppenheimer approximation used to separate the motion of the nuclei from
that of the electrons, so that the problem is reduced to that of solving
the equations of motion for an electron gas in a static potential.
The consequences of the indistinguishability of identical particles are then
discussed, as well as results of the relativistic theory of quantum
mechanics which need to be included by hand in our non-relativistic
treatment. Finally the powerful variational
principle is introduced which is often used in solving the equations of
quantum mechanics.

- 2.1 Principles of quantum mechanics
- 2.2 The Born-Oppenheimer approximation
- 2.3 Identical particles
- 2.4 Variational principles

Peter Haynes