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

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

2001-09-03

arxiv.org/abs/hep-th/0109003v2

Int.J.Mod.Phys. A19 (2004) 1413-1440

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1142/S0217751X04017926

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.

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