---
_id: '45763'
abstract:
- lang: eng
  text: |-
    <jats:title>Abstract</jats:title>
                   <jats:p>The development of potential theory heightens the understanding of fundamental interactions in quantum systems. In this paper, the bound state solution of the modified radial Klein-Gordon equation is presented for generalised tanh-shaped hyperbolic potential from the Nikiforov-Uvarov method. The resulting energy eigenvalues and corresponding radial wave functions are expressed in terms of the Jacobi polynomials for arbitrary $l$ states. It is also demonstrated that energy eigenvalues strongly correlate with potential parameters for quantum states. Considering particular cases, the generalised tanh-shaped hyperbolic potential and its derived energy eigenvalues exhibit good agreement with the reported findings. Furthermore, the rovibrational energies are calculated for three representative diatomic molecules, namely $\rm{H_{2}}$, $\rm{HCl}$ and $\rm{O_{2}}$. The lowest excitation energies are in perfect agreement with experimental results. Overall, the potential model is displayed to be a viable candidate for concurrently prescribing numerous quantum systems.</jats:p>
author:
- first_name: Vatan
  full_name: Badalov, Vatan
  last_name: Badalov
- first_name: Sabuhi
  full_name: Badalov, Sabuhi
  last_name: Badalov
citation:
  ama: 'Badalov V, Badalov S. Generalised tanh-shaped hyperbolic potential: Klein-Gordon
    equation’s bound state solution. <i>Communications in Theoretical Physics</i>.
    Published online 2023. doi:<a href="https://doi.org/10.1088/1572-9494/acd441">10.1088/1572-9494/acd441</a>'
  apa: 'Badalov, V., &#38; Badalov, S. (2023). Generalised tanh-shaped hyperbolic
    potential: Klein-Gordon equation’s bound state solution. <i>Communications in
    Theoretical Physics</i>. <a href="https://doi.org/10.1088/1572-9494/acd441">https://doi.org/10.1088/1572-9494/acd441</a>'
  bibtex: '@article{Badalov_Badalov_2023, title={Generalised tanh-shaped hyperbolic
    potential: Klein-Gordon equation’s bound state solution}, DOI={<a href="https://doi.org/10.1088/1572-9494/acd441">10.1088/1572-9494/acd441</a>},
    journal={Communications in Theoretical Physics}, publisher={IOP Publishing}, author={Badalov,
    Vatan and Badalov, Sabuhi}, year={2023} }'
  chicago: 'Badalov, Vatan, and Sabuhi Badalov. “Generalised Tanh-Shaped Hyperbolic
    Potential: Klein-Gordon Equation’s Bound State Solution.” <i>Communications in
    Theoretical Physics</i>, 2023. <a href="https://doi.org/10.1088/1572-9494/acd441">https://doi.org/10.1088/1572-9494/acd441</a>.'
  ieee: 'V. Badalov and S. Badalov, “Generalised tanh-shaped hyperbolic potential:
    Klein-Gordon equation’s bound state solution,” <i>Communications in Theoretical
    Physics</i>, 2023, doi: <a href="https://doi.org/10.1088/1572-9494/acd441">10.1088/1572-9494/acd441</a>.'
  mla: 'Badalov, Vatan, and Sabuhi Badalov. “Generalised Tanh-Shaped Hyperbolic Potential:
    Klein-Gordon Equation’s Bound State Solution.” <i>Communications in Theoretical
    Physics</i>, IOP Publishing, 2023, doi:<a href="https://doi.org/10.1088/1572-9494/acd441">10.1088/1572-9494/acd441</a>.'
  short: V. Badalov, S. Badalov, Communications in Theoretical Physics (2023).
date_created: 2023-06-24T19:40:20Z
date_updated: 2023-06-24T19:40:56Z
doi: 10.1088/1572-9494/acd441
keyword:
- Physics and Astronomy (miscellaneous)
publication: Communications in Theoretical Physics
publication_identifier:
  issn:
  - 0253-6102
  - 1572-9494
publication_status: published
publisher: IOP Publishing
status: public
title: 'Generalised tanh-shaped hyperbolic potential: Klein-Gordon equation''s bound
  state solution'
type: journal_article
user_id: '78800'
year: '2023'
...