An Alternate Approach to Transition Potentials

1993/05/18 by Asim Gangopadhyaya, Prasanta K. Panigrahi, Gangopadhyaya, Asim +3
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)

paper · pdf · doi:10.48550/arxiv.hep-th/9305082

openalex publication_date 1993/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analyze transition potentials (V(r) \stackrelr∼ 0→ αr^-2) in non-relativistic quantum mechanics using the techniques of supersymmetry. For the range -1/4 < α< 3/4, the eigenvalue problem becomes ill-defined (since it is not possible to choose a unique eigenfunction based on square integrability and boundary conditions). It is shown that supersymmetric quantum mechanics (SUSYQM) provides a natural prescription for a unique determination of the spectrum. Interestingly, our SUSYQM based approach picks out the same "less singular" wave functions as the conventional approach, and thus provides a simple justification for the usual practice in the literature. Two examples (the Pöschl-Teller II potential and a two anyon system on the plane) have been worked out for illustrative purposes.

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