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

2024/01/02 by Satish Kumar Yadav, Rahul Ghosh, Yadav, Satish +3
Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2401.00995

openalex publication_date 2024/01/02 · openalex created_date 2024/01/04 · openalex updated_date 2026/07/28

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 Schrödinger equation in the PDM framework by considering two different fairly generic position-dependent masses (i) M(x)=λg'(x) and (ii) M(x) = c ( g'(x) )^ν, ν=(2η)/(2η+1), with η= 0,1,2⋯ . 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 (ν) 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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