On recurrence relations for radial wave functions for the $N$-th dimensional oscillators and hydrogenlike atoms: analytical and numerical study

R. Álvarez-Nodarse, J. L. Cardoso, and N. R. Quintero

Abstract

Using a general procedure for finding recurrence relations for hypergeometric functions and polynomials introduced by Cardoso et al. [J. Phys. A, 36 (2003), pp. 2055-2068] we obtain some new recurrence relations for the radial wave functions of the $N$-th dimensional isotropic harmonic oscillators as well as the hydrogenlike atoms. A numerical analysis of such recurrences is also presented.

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Key words

wave functions, linear recurrence relations, Laguerre polynomials

AMS subject classifications

33C45, 11B37, 81V45, 81Q99