Non-Hermitian Hamiltonians, Decaying States, and Perturbation Theory

The conventional time-independent perturbation theory and projection-operator techniques are generalized to systems propagating under the influence of an effective non-Hermitian Hamiltonian, e.g., an optical-model potential. The mathematical complications which can arise due to lack of orthogonality and completeness for the eigenstates of such a Hamiltonian are discussed on an elementary level. Examples of the various techniques involved are taken from considerations of models for exotic atoms and cascade processes.