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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.


Peter Haynes