Periodic Quasi - Exactly Solvable Models

Abstract

Various quasi-exact solvability conditions, involving the parameters of the periodic associated Lam{é} potential, are shown to emerge naturally in the quantum Hamilton-Jacobi approach. It is found that, the intrinsic nonlinearity of the Riccati type quantum Hamilton-Jacobi equation is primarily responsible for the surprisingly large number of allowed solvability conditions in the associated Lam{é} case. We also study the singularity structure of the quantum momentum function, which yields the band edge eigenvalues and eigenfunctions.

11 pages, 5 tables

References in corpus (4)

• Some Exact Results for Mid-Band and Zero Band-Gap States of Associated Lame Potentials
• A Study of Quasi-Exactly Solvable Models within the Quantum Hamilton-Jacobi Method
• Associated Lame and various other new classes of elliptic potentials from sl(2,R) and related orthogonal polynomials
• Calculation of Band Edge Eigenfunctions and Eigenvalues of Periodic Potentials through the Quantum Hamilton - Jacobi Formalism

Cited by in corpus (3)

• The Quantum Effective Mass Hamilton-Jacobi Problem
• Shape invariance and the exactness of quantum Hamilton-Jacobi formalism
• Supersymmetric partners for the associated Lame potentials