A new family of shape invariantly deformed Darboux-Pöschl-Teller potentials with continuous \ell

Details A new family of shape invariantly deformed Darboux-Pöschl-Teller potentials with continuous \ell A new family of shape invariantly deformed Darboux-Pöschl-Teller potentials with continuous \ell

2010-07-22

arxiv.org/abs/1007.3800v2

J.Phys.A44:195203,2011

Physics

Mathematical Physics

19 pages. Sec.5(Summary and Comments): one sentence added in the first paragraph, several sentences modified in the last parag

Scientific paper

10.1088/1751-8113/44/19/195203

We present a new family of shape invariant potentials which could be called a ``continuous \ell version" of the potentials corresponding to the exceptional (X_{\ell}) J1 Jacobi polynomials constructed recently by the present authors. In a certain limit, it reduces to a continuous \ell family of shape invariant potentials related to the exceptional (X_{\ell}) L1 Laguerre polynomials. The latter was known as one example of the `conditionally exactly solvable potentials' on a half line.

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