Recurrence relations for radial wavefunctions for theNth-dimensional oscillators and hydrogenlike atoms

Abstract

We present a general procedure for finding recurrence relations of the radial wavefunctions for Nth-dimensional isotropic harmonic oscillators and hydrogenlike atoms.

Exactly Complete Solutions of the Pseudoharmonic Potential in N-Dimensions

“…Some of the physical systems of interest in quantum mechanics that have been thoroughly studied in N -dimensional space are the two common exactly solvable potentials, these are, the harmonic and Coulomb potentials [4,16,19,21,22,25,26,28,64,67,77,78,84,87,91,108,111].…”

“…Among these are the investigation carried out on the relationship between a Coulomb and a harmonic oscillator potentials in arbitrary dimensions by [16,19,22,25,28,64,67,77,78,91,108,111], followed by comments of ( [91] and [77]) on the work of [16].…”

Recurrence relations for discrete hypergeometric functions

“…Let us point out that for getting the polynomial coefficients B i , i = 1, 2, 3 in (3.17) (or A i , i = 1, 2, 3 in (4.12)) we will follow the idea in [16]. Given m, the idea is to identify the corresponding relation (3.17) (or (4.12)) with one of the known expressions (2.13)-(2.18) for the classical polynomials.…”

“…The main idea is to use the connection of the wave functions with the classical discrete polynomials in a similar way as it was done in our previous paper [16] for the N -th dimensional oscillators and hydrogenlike atoms. This approach allows us to recover the relations obtained in [5,19,20] and also to obtain several new relations for the discrete polynomials and therefore for the associated (wave) functions in a constructive way.…”

Fisher information of special functions and second-order differential equations

“…This approach has been pioneered by Arnold F. Nikiforov and Vasilii B. Uvarov [36] who developed an elegant technique to determine numerous algebraic properties of the hypergeometric-type functions and some generalized hypergeometric-type functions. This technique, which works when the polynomial coefficients σ(x) and τ (x) do not depend on the spectral parameter λ [58], was later on developed and extended to find linear and non-linear recurrence relations for hypergeometric-type functions with three and four terms [17-19, 58, 59] and applied to some quantum-mechanical problems [3,4]. Just recently, it has been generalized to the case when the polynomial coefficients of Eq.…”