Exactly solvable associated Lamé potentials and supersymmetric transformations

2006/08/23 by David J. Fernandez C., David J. Fernández, Asish Ganguly · 21 citations
Mathematics · Physics and Astronomy · #Energy (signal processing) #Exact solutions in general relativity #Factorization #Mathematical functions and polynomials #Nonlinear Waves and Solitons #Property (philosophy) #Quantum Mechanics and Non-Hermitian Physics #Supersymmetry #Value (mathematics) #hep-th #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1016/j.aop.2006.07.011

published in Annals of Physics 322(5), 1143-1161 (Elsevier BV) · Annals of Phys.(in press); Present e-mail of AG: [email protected]

arxiv created 2006/08/23 · openalex publication_date 2006/09/12 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

A systematic procedure to derive exact solutions of the associated Lame equation for an arbitrary value of the energy is presented. Supersymmetric transformations in which the seed solutions have factorization energies inside the gaps are used to generate new exactly solvable potentials; some of them exhibit an interesting property of periodicity defects.

Citations

• BAND EDGE EIGENFUNCTIONS AND EIGENVALUES FOR PERIODIC POTENTIALS THROUGH THE QUANTUM HAMILTON–JACOBI FORMALISM
• New solvable and quasiexactly solvable periodic potentials
• New supersymmetric partners for the associated Lamé potentials
• ASSOCIATED LAMÉ EQUATION, PERIODIC POTENTIALS AND sl(2, ℝ)
• Nonlocal supersymmetric deformations of periodic potentials
• A new family of N-fold supersymmetry: type B
• A SUSY approach for investigation of two-dimensional quantum mechanical systems