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

References in corpus (11)

• An Alternative to Compactification
• Singular Potentials and Limit Cycles
• Renormalization in Quantum Mechanics
• Renormalization of the Inverse Square Potential
• Quantum Anomaly in Molecular Physics
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• A Neutral Atom and a Charged Wire: From Elastic scattering to Absorption
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• Regularized Green's Function for the Inverse Square Potential
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• Renormalization in conformal quantum mechanics
• Spectral Properties of the Symmetry Generators of Conformal Quantum Mechanics: A Path-Integral Approach
• Nonrelativistic scale anomaly, and composite operators with complex scaling dimensions
• Conformal quantum mechanics of causal diamonds: Time evolution, thermality, and instability via path integral functionals
• Quantum aspects of spacetime: A quantum optics view of acceleration radiation and black holes
• Non-entropic theory of rubber elasticity: flexible chains with weak excluded-volume interactions