Path Integral Treatment of Singular Problems and Bound States: Quantum Mechanics

Abstract

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 analogue of ultraviolet regularization is required for the interpretation of these singular problems.

32 pages. The paper was significantly expanded and numerous equations were added for the sake of clarity; the main results and conclusions are unchanged