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arXiv:math-ph/0401041 · Journal of Physics A Mathematical and General

Conditionally exactly solvable potential and dual transformation in quantum mechanics

Bijan Kumar Bagchi, C. Quesne

Published Mar 9, 2004• 6 citations
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Abstract

We show that the conditionally exactly solvable potential of Dutt et al (1995 J. Phys. A: Math. Gen. 28 L107) and the exactly solvable potential from which it is derived form a dual system.
DOI
10.1088/0305-4470/37/12/l02

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We detect an omission in the paper ``Conditionally exactly soluble class of quantum potentials'' by A. de Souza Dutra [Phys. Rev. A 47, R2435 (1993)]. There, two strongly singular s-wave bound-state problems have been claimed completely solvable in closed form. Unfortunately, all the displayed wave functions are merely asymptotically correct solutions which do not satisfy the appropriate threshold boundary condition. We show that the incorporation of the threshold boundary conditions only leads to a very partial exact solvability at a single energy and for special couplings.
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