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

DOI10.1063/1.1509852zbMath1060.81014arXivmath-ph/0212045OpenAlexW1994688918MaRDI QIDQ4832796

Asish Ganguly

Publication date: 14 December 2004

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0212045

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Exactly and quasi-solvable systems arising in quantum theory (81U15)

Cites Work

• Supersymmetry breaking with periodic potentials
• Duality and self-duality (Energy reflection symmetry) of quasi-exactly solvable periodic potentials
• Quasi-exactly-solvable problems and sl(2) algebra
• ASSOCIATED LAMÉ EQUATION, PERIODIC POTENTIALS AND sl(2, ℝ)
• GENERATING COMPLEX POTENTIALS WITH REAL EIGENVALUES IN SUPERSYMMETRIC QUANTUM MECHANICS
• Lame equation, sl(2) algebra and isospectral deformations
• A search for shape-invariant solvable potentials
• A new algebraization of the Laméequation
• New solvable and quasiexactly solvable periodic potentials
• Associated Lamé and various other new classes of elliptic potentials from sl(2,R) and related orthogonal polynomials
• Quasi-exactly solvable systems and orthogonal polynomials
• Quasi-exactly solvable potentials on the line and orthogonal polynomials

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