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STATIONARY AND NONSTATIONARY QUANTUM PROBLEMS SOLUBLE BY THE CONTOUR INTEGRAL TECHNIQUE.

Yu. N. Demkov, Vladimir I. Osherov

Published Jan 1, 1967• 1 citation
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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)
A path-integral approach for the computation of quantum-mechanical propagators and energy Green's functions is presented. Its effectiveness is demonstrated through its application to singular interactions, with particular emphasis on the inverse square potential — possibly combined with a delta-function interaction. The emergence of these singular potentials as low-energy nonrelativistic limits of quantum field theory is highlighted. Not surprisingly, the analog of ultraviolet regularization is required for the interpretation of these singular problems.