Approximating Quantum Systems

Abstract

Several approximations were already carried out in earlier chapters. In this respect, for example in Chapter 7, we have considered relativistic corrections to the energy levels of the hydrogen atom, also the non-relativistic Lamb shift, and treated the atom in external electromagnetic fields. In Chapter 8, we have discussed the validity of the exponential law in a two-level system (§8.1) and related approximations involved. In the same chapter, radiation loss in spin precession was studied (§8.4), a computation of the anomalous magnetic moment of the electron was made (§8.5), the problem of quantum decoherence by the environment was considered (§8.7, §8.9) and the so-called geometric phase in the adiabatic approximating regime was investigated (§8.13). Some approximations are also given in Chapter 15 on quantum scattering, just to mention a few of the applications of approximation methods. The present chapter supplements these studies by investigating the nature of several approximation procedures, some of which are related to the above applications in other chapters. Accordingly, the latter material may be read in conjunction with the present one.