Exceptional orthogonal polynomials and exactly solvable potentials in position dependent mass Schrödinger Hamiltonians

2009/09/20 by Bikashkali Midya, Barnana Roy · 94 citations
Mathematics · Physics and Astronomy · #Bound state #Classical orthogonal polynomials #Invariant (physics) #Isospectral #Jacobi polynomials #Laguerre polynomials #Mathematical analysis #Mathematical functions and polynomials #Mathematical physics #Mathematics #Orthogonal polynomials #Physics #Position (finance) #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Upper and lower bounds #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1016/j.physleta.2009.09.030

published in Physics Letters A 373(45), 4117-4122 (Elsevier BV) · To appear in Physics Letters A

openalex publication_date 2009/09/20 · arxiv created 2009/10/07 · arxiv updated 2015/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Some exactly solvable potentials in the position dependent mass background are generated whose bound states are given in terms of Laguerre- or Jacobi-type X₁ exceptional orthogonal polynomials. These potentials are shown to be shape invariant and isospectral to the potentials whose bound state solutions involve classical Laguerre or Jacobi polynomials.

Citations

• Shape-invariant quantum Hamiltonian with position-dependent effective mass through second-order supersymmetry
• Supersymmetry and Quantum Mechanics
• Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry
• SUPERSYMMETRIC APPROACH TO EXACTLY SOLVABLE SYSTEMS WITH POSITION-DEPENDENT EFFECTIVE MASSES
• EXACT SOLUTIONS OF EFFECTIVE-MASS SCHRÖDINGER EQUATIONS
• First-order intertwining operators and position-dependent mass Schrödinger equations in d dimensions

Cited by

• Position-dependent mass, finite-gap systems, and supersymmetry