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Zbl 0970.81014
Negro, J.; Nieto, L.M.; Rosas-Ortiz, O.
Confluent hypergeometric equations and related solvable potentials in quantum mechanics. (English)
[J] J. Math. Phys. 41, No.12, 7964-7996 (2000). ISSN 0022-2488; ISSN 1089-7658/e

Summary: The connection between the Schrödinger and confluent hypergeometric equations is discussed. It is shown that the factorization of the confluent hypergeometric equation gives a unifying powerful algebraic tool in order to study some quantum mechanical eigenvalue problems. That description includes the linear and $N$-dimensional harmonic oscillators, as well as the Coulomb and Morse potentials.

MSC 2000:: *81Q05 Closed and approximate solutions to quantum-mechanical equations
33C10 Cylinder functions, etc.

Keywords: $N$-dimensional harmonic oscillators; eigenvalue problems; Morse potentials; Coulomb potential

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