Shape invariance, raising and lowering operators in hypergeometric type equations

Details Shape invariance, raising and lowering operators in hypergeometric type equations Shape invariance, raising and lowering operators in hypergeometric type equations

2002-06-19

arxiv.org/abs/quant-ph/0206129v1

Physics

Quantum Physics

LaTeX 2.09, 11 pages, IOP style (Bristol), All is included in only one .tex file, Please use for reply my e-address: ncotfas@y

Scientific paper

10.1088/0305-4470/35/44/306

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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