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arXiv · 2401.00995

New solutions of Isochronous potentials in terms of exceptional orthogonal polynomials in heterostructures

Satish Yadav·Rahul Ghosh·Bhabani Prasad Mandal
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Abstract

Point canonical transformation (PCT) has been used to find out new exactly solvable potentials in the position-dependent mass (PDM) framework. We solve $1$-D Schr\"{o}dinger equation in the PDM framework by considering two different fairly generic position-dependent masses $ (i) M(x)=\lambda g'(x)$ and $(ii) M(x) = c \left( {g'(x)} \right)^\nu $, $\nu =\frac{2\eta}{2\eta+1},$ with $\eta= 0,1,2\cdots $. In the first case, we find new exactly solvable potentials that depend on an integer parameter $m$, and the corresponding solutions are written in terms of $X_m$-Laguerre polynomials. In the latter case, we obtain a new one parameter $(\nu)$ family of isochronous solvable potentials whose bound states are written in terms of $X_m$-Laguerre polynomials. Further, we show that the new potentials are shape invariant by using the supersymmetric approach in the framework of PDM.

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Satish Yadav, Rahul Ghosh, Bhabani Prasad Mandal. 2024-01-02. New solutions of Isochronous potentials in terms of exceptional orthogonal polynomials in heterostructures. https://arxiv.org/abs/2401.00995

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