An improved quantum condition for the bound state problem in non-relativistic quantum mechanics using the NUFA method

P. Rajesh Kumar

doi:10.1140/epjp/s13360-021-02234-w

EPJ

An improved quantum condition for the bound state problem in non-relativistic quantum mechanics using the NUFA method

P. Rajesh Kumar^a

Faculty of Applied Sciences, Open University Malaysia, Jalan SS 7/19, Kelana Jaya, 47301, Petaling Jaya, Selangor, Malaysia

^a This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 20 October 2021
Accepted: 27 November 2021
Published online: 10 December 2021

Abstract

The bound state is an intriguing quantum mechanics problem. In this paper, an improved and elegant quantum condition for the bound state problem in non-relativistic quantum mechanics using the Nikiforov-Uvarov functional analysis (NUFA) method is presented. From the quantum condition, two simple formulas are obtained to calculate the energy spectrum for the bound state problem, one for the case when the parameter

α_{3} \neq 0

$\alpha_{3} \ne 0$ and the other when

α_{3} \to 0

$\alpha_{3} \to 0$ . The corresponding eigenstates are also derived in terms of hypergeometric functions. Two bound state problems are studied using the improved quantum condition.

International School of Cosmic Ray Astrophysics
24th Course: “Particles and the Cosmos”
29 July – 6 August 2026
Erice, Italy

EPJ

An improved quantum condition for the bound state problem in non-relativistic quantum mechanics using the NUFA method

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