New classes of quasi-solvable potentials, their exactly-solvable limit and related orthogonal polynomials

Abstract

We have generated, using an sl(2,R) formalism, several new classes of quasi-solvable elliptic potentials, which in the appropriate limit go over to the exactly solvable forms. We have obtained exact solutions of the corresponding spectral problems for some real values of the potential parameters. We have also given explicit expressions of the families of associated orthogonal polynomials in the energy variable.

14 pages, 5 tables, LaTeX2e

References in corpus (5)

• Generating Complex Potentials with Real Eigenvalues in Supersymmetric Quantum Mechanics
• Duality and Self-Duality (Energy Reflection Symmetry) of Quasi-Exactly Solvable Periodic Potentials
• Some Exact Results for Mid-Band and Zero Band-Gap States of Associated Lame Potentials
• Associated Lame and various other new classes of elliptic potentials from sl(2,R) and related orthogonal polynomials
• Associated LamÉ Equation, Periodic Potentials and sl(2,R)

Cited by in corpus (7)

• An extended class of L2-series solutions of the wave equation
• Shape-invariant quantum Hamiltonian with position-dependent effective mass through second order supersymmetry
• A unified treatment of exactly solvable and quasi-exactly solvable quantum potentials
• A new effective mass Hamiltonian and associated Lame equation: bound states
• Exactly solvable associated Lame potentials and supersymmetric transformations
• New supersymmetric partners for the associated Lame potentials
• L2 series solutions of the Dirac equation for power-law potentials at rest mass energy