A New Special Function with Applications to Quantum Mechanics





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


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.


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How to Cite

Chinchole, S. M. (2024). A New Special Function with Applications to Quantum Mechanics. Communications in Mathematics and Applications, 14(5), 1479–1492. https://doi.org/10.26713/cma.v14i5.1840



Research Article