A New Special Function with Applications to Quantum Mechanics

S. M. Chinchole

doi:10.26713/cma.v14i5.1840

Authors

S. M. Chinchole Department of Mathematics, Mahatma Gandhi Vidyamandir’s Arts, Science and Commerce College, Manmad, Maharashtra, India https://orcid.org/0000-0003-1670-4814 (unauthenticated)

DOI:

https://doi.org/10.26713/cma.v14i5.1840

Keywords:

Sturm-Liouville differential equation, Bessel Function, Special Function, Laplace equation, Schrödinger equation

Abstract

In this paper, a special function using the particular Sturm-Liouville Equation is introduced. Sequences of recurrence relations are presented for that special function. Also, its series and definite integral representations are provided. This special function is a radial solution to the Laplace equation in the 5-dimensional hyperspherical coordinate system. It is also a solution to the 4-dimensional Radial Schrödinger equation. All results are verified numerically using different mathematical softwares.

826 584

Downloads

Download data is not yet available.

References

M. Abu-Shady, T.A. Abdel-Karim and E.M. Khokha, Exact solution of the N-dimensional radial Schrödinger equation via Laplace transformation method with the generalized Cornell potential, arXiv preprint arXiv:1802.02092 (2018), DOI: 10.48550/arXiv.1802.02092.

V.A. Andreev and D. Yu. Tsipenyuk, The 5-dimensional model for electromagnetism and gravity, Natural Science 6(4) (2014), 248 – 253, DOI: 10.4236/ns.2014.64028.

L.C. Andrews and B.K. Shivamogg, Integral Transforms for Engineers, SPIE Press (1999), DOI: 10.1117/3.339204.

J.E. Avery and J.S. Avery, Hyperspherical Harmonics and Their Physical Applications, World Scientific (2017), DOI: 10.1142/10690.

W.W. Bell, Special Functions for Scientists and Engineers, Illustrated edition, Dover Books on Mathematics series, Dover Publications Inc., 272 pages (2004), DOI: 10.2307/3613224.

R. Cicchetti and A. Faraone, Incomplete Hankel and modified Bessel functions: a class of special functions for electromagnetics, IEEE Transactions on Antennas and Propagation 52(12) (2004), 3373 – 3389, DOI: 10.1109/TAP.2004.835269.

A. Jirari, Second-order Sturm-Liouville difference equations and orthogonal polynomials, Memoirs of the American Mathematical Society 113(542) (1995), DOI: 10.1090/memo/0542.