Quantum Mechanics II

Abstract

This chapter addresses those students who seek a more detailed knowledge of quantum-mechanical applications to systems of general interest. The first part presents various aspects of scattering theory: Green functions, the Lippmann–Schwinger equation, the Born approximation, Möller’s wave operator, scattering and transition operators, both two- and three-body scattering, the Gell-Mann–Goldberger formula, Feshbach’s theory of nuclear reactions, the Breit–Wigner formula, the Faddeev equations, and (un)connected Feynman graphs. The second part is devoted to many-particle systems of fermions, bosons, and photons, the Hartree–Fock equations, the BCS formalism, the Bogoliubov transformation, electric field quantization (rarely found elsewhere), Glauber states, and quenched states. Coupled photon–electron states (polaritons) and the excitation and de-excitation of atoms in a light field (Jaynes–Cummings model), are also rarely found elsewhere. In the third part, we treat the Dirac equation. Results are given in the Weyl representation, which is preferred here, but also in the standard representation. The particle–antiparticle versus particle–hole controversy is taken up, something still under dispute.

List of Symbols

We stick closely to the recommendations of the International Union of Pure and Applied Physics (IUPAP) and the Deutsches Institut für Normung (DIN). These are listed in Symbole, Einheiten und Nomenklatur in der Physik (Physik-Verlag, Weinheim 1980) and are marked here with an asterisk. However, one and the same symbol may represent different quantities in different branches of physics. Therefore, we have to divide the list of symbols into different parts (Table 5.3).

Table 5.3 Symbols used in quantum mechanics II