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An Alternate Approach to Transition Potentials | | Asim Gangopadhyaya
; Prasanta K. Panigrahi
; Uday P. Sukhatme
; | | Date: |
18 May 1993 | | Subject: | hep-th | | Abstract: | We analyze transition potentials $(V(r) stackrel{rsim 0}{
ightarrow} {alpha r^{-2}})$ in non-relativistic quantum mechanics using the techniques of supersymmetry. For the range $-1/4 < alpha < 3/4$, 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. | | Source: | arXiv, hep-th/9305082 | | Services: | Forum | Review | PDF | Favorites | |
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