Shape invariance, raising and lowering operators in hypergeometric type equations

Abstract

The Schr\" odinger equations which are exactly solvable in terms of associated special functions are directly related to some self-adjoint operators defined in the theory of hypergeometric type equations. The fundamental formulae occurring in a supersymmetric approach to these Hamiltonians are consequences of some formulae concerning the general theory of associated special functions. We use this connection in order to obtain a general theory of Schr\" odinger equations exactly solvable in terms of associated special functions, and to extend certain results known in the case of some particular potentials.

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References in corpus (5)

• Temporally stable coherent states for infinite well and Pöschl-Teller potentials
• Raising and lowering operators, factorization and differential/difference operators of hypergeometric type
• Generalized coherent and intelligent states for exact solvable quantum systems
• Continuous vs. discrete models for the quantum harmonic oscillator and the hydrogen atom
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Cited by in corpus (7)

• Systems of orthogonal polynomials defined by hypergeometric type equations with application to quantum mechanics
• Orthogonal polynomials defined by hypergeometric type equations with application to quantum mechanics
• A search on the Nikiforov-Uvarov formalism
• Hypergeometric type operators and their supersymmetric partners
• Systems of orthogonal polynomials defined by hypergeometric type equations
• Associated special functions and coherent states
• Algorithm for generating new explicitly solvable Schrodinger type equations