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PATH INTEGRAL TREATMENT OF SINGULAR PROBLEMS AND BOUND STATES

Department of Physics, University of San Francisco, San Francisco, California 94117-1080, USA

and

Department of Physics, University of Houston, University of Houston Center, Houston, Texas 77204-5506, USA

World Laboratory Center for Pan-American Collaboration in Science and Technology, University of Houston Center, Houston, Texas 77204-5506, USA

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https://doi.org/10.1142/S0217751X04017926Cited by:4 (Source: Crossref)

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

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