General Laws of Optical Transitions

Abstract

Selection rules and symmetry considerations play a basic role in modern physics. This holds for the atomic shells, the nucleus, elementary particles and for many other areas. We shall present only a small but typical sample here, taking up the perturbation theory discussed in Sect. 15.2. We began with the unperturbed wavefunctions ø _n . The perturbation Hamiltonian in one example contained the dipole moment ez. In the following, we shall first choose the x coordinate instead of the z coordinate. We became acquainted with matrix elements of the form

$$/[H_{mn}^\text{P} = \int {\phi _m^* (r)ex\phi _n (r)dV} ]/$$

((16.1))

as important parameters. As we observed at that time, there are a number of realistic cases in which matrix elements vanish when the indices m and n are equal, on the basis of symmetry alone. We shah now examine these cases.