Approximation Methods for Bound States

Iraj R. Afnan

With a limit on the small number of problems that admit exact solutions, we turn in this chapter to approximation methods that can be used for bound state problems. The most commonly used method is the perturbation theory for which one use a small parameter to form the basis of a systematic expansion, or a variational method in which one hopes to set the best limit on the energy of a system. We will consider both of these approximation methods with applications to problems in atomic and molecular physics.

Alain Decoster

The conditions of validity for the momentum-translation approximation of Reiss are found much more stringent than was thought before: multiphotonic transitions induced by one strong field cannot be described by this method. First-order transitions between bound states dressed by a strong low-frequency field can be calculated, but the method gives nothing but a trivial result; only for the ionization of a dressed atom is the approximation found useful.

Charles G. Wohl

Saverio Bivona, R. Burlon, C Leone

We show that by using the approximation method of Bivona et al , two-colour photodetachment cross sections are obtained that behave according to the Wigner threshold law even if the dressing effect of the low-frequency radiation field on the bound state is ignored. Within the range of the low frequency and intensity of the radiation field considered, it is found that the values of the cross sections calculated by using the field-free bound state are not significantly modified when the corrections to the wavefunction of the bound state due to the driving action of the low-frequency field are accounted for.