PERTURBATION-THEORY ON GENERALIZED QUANTUM-MECHANICAL SYSTEMS

We present a general formalism for doing the perturbation theory in th e complex energy plane, where the notion of the generalized quantum me chanical systems is used. This formalism is applied to the Friedrichs- Lee model. It reproduces the results of the exact solution, where the spectrum of the generalized quantum mechanical system consists of a di screte complex energy pole and a continuum spectrum (which passes belo w this discrete pole) in the complex energy plane. We also investigate the role of the ''complex delta'' function in the description of a re sonance state. The unboundedness of the spectrum appears to be the ver y ingredient needed to give rise to a pure exponential decay.