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Physics Letters A

On a variational principle for decaying states

Gy. I. Szász

Published Jan 1, 1976• 8 citations
Publisher
DOI
10.1016/0375-9601(76)90690-3

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A variational principle is formulated which is invariant with respect to normalization of wave functions and which can be used in the case of nonorthogonal wave functions of the initial and final states. The problera of uniqueness of perturbation theory in this case is considered. The possibility of employing the variational principle for solution of problems concerning decay of the quasi-stationary state and charge exchange is discussed. The main equations for charge exchange at large impact parameters are derived from the variational principle. (auth)

•Jun 1, 1960•0 citations
The Hamiltonian of a system containing decaying states is subjected to a nonunitary similarity transformation which introduces the wave functions of these decaying states as well as those of the "antidecaying" dual states explicitly into the representation. The dependence of the Green's-function pole on these wave functions is used to formulate a variational principle for their determination, yielding a non-Hermitian, nonlinear wave equation including self-energy contributions. Explicit solutions are given in a simple example.
A variational principle is formulated which is invariant with respect to normalization of wave functions and which can be used in the case of nonorthogonal wave functions of the initial and final states. The problera of uniqueness of perturbation theory in this case is considered. The possibility of employing the variational principle for solution of problems concerning decay of the quasi-stationary state and charge exchange is discussed. The main equations for charge exchange at large impact parameters are derived from the variational principle. (auth)