ASSOCIATED LAMÉ EQUATION, PERIODIC POTENTIALS AND sl(2, ℝ)

2000/10/10 by Asish Ganguly, ASISH GANGULY · 18 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Eigenfunction #Energy (signal processing) #Enhanced Data Rates for GSM Evolution #Integer (computer science) #Mathematical functions and polynomials #Quantum Mechanics and Non-Hermitian Physics #Spectral line #Spectrum (functional analysis) #hep-th #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1142/s0217732300002346

published in Modern Physics Letters A 15(31), 1923-1930 (World Scientific) · 8 pages, no figure, tex file(version 2.09)

openalex publication_date 2000/10/10 · arxiv created 2002/04/11 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We propose a new approach based on the algebraization of the associated Lamé equation [Formula: see text] within sl(2, ℝ) to derive the corresponding periodic potentials. The band edge eigenfunctions and energy spectra are explicitly obtained for integers m, l. We also obtain the explicit expressions of the solutions for half-integer m and integer or half-integer l.

Citations

• An exactly soluble Schrödinger equation with a bistable potential

Cited by

• Soliton lattice and single soliton solutions of the associated Lamé and Lamé potentials
• Exactly solvable associated Lamé potentials and supersymmetric transformations