Comprehensive analysis of conditionally exactly solvable models

Details Comprehensive analysis of conditionally exactly solvable models Comprehensive analysis of conditionally exactly solvable models

2001-02-16

arxiv.org/abs/math-ph/0102017v1

J. Math. Phys. 42 (2001) 1996 - 2007

Physics

Mathematical Physics

19 pp, 1 fig., to appear in J. Math. Phys. http://ojps.aip.org/journals/doc/JMAPAQ-home/top.jsp

Scientific paper

10.1063/1.1362286

We study a quantum mechanical potential introduced previously as a conditionally exactly solvable (CES) model. Besides an analysis following its original introduction in terms of the point canonical transformation, we also present an alternative supersymmetric construction of it. We demonstrate that from the three roots of the implicit cubic equation defining the bound-state energy eigenvalues, there is always only one that leads to a meaningful physical state. Finally we demonstrate that the present CES interaction is, in fact, an exactly solvable Natanzon-class potential.

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