https://doi.org/10.1140/epjp/s13360-021-02234-w
Regular Article
An improved quantum condition for the bound state problem in non-relativistic quantum mechanics using the NUFA method
Faculty of Applied Sciences, Open University Malaysia, Jalan SS 7/19, Kelana Jaya, 47301, Petaling Jaya, Selangor, Malaysia
Received:
20
October
2021
Accepted:
27
November
2021
Published online:
10
December
2021
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 
and the other when 
. The corresponding eigenstates are also derived in terms of hypergeometric functions. Two bound state problems are studied using the improved quantum condition.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021
