Ro-vibrational energy analysis of Manning-Rosen and P\"oschl-Teller potentials with a new improved approximation in the centrifugal term

• URL: http://arxiv.org/abs/2205.10313v1
• Date: Thu, 19 May 2022 15:58:30 GMT
• Title: Ro-vibrational energy analysis of Manning-Rosen and P\"oschl-Teller potentials with a new improved approximation in the centrifugal term
• Authors: Debraj Nath and Amlan K. Roy
• Abstract summary: Two physically important potentials (Manning-Rosen and P"oschl-Teller) are considered for the ro-vibrational energy in diatomic molecules. An improved new approximation is invoked for the centrifugal term, which is then used for their solution within the Nikiforov-Uvarov framework.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Two physically important potentials (Manning-Rosen and P\"oschl-Teller) are considered for the ro-vibrational energy in diatomic molecules. An improved new approximation is invoked for the centrifugal term, which is then used for their solution within the Nikiforov-Uvarov framework. This employs a recently proposed scheme, which combines the two widely used Greene-Aldrich and Pekeris-type approximations. Thus, approximate analytical expressions are derived for eigenvalues and eigenfunctions. The energies are examined with respect to two approximation parameters, $\lambda$ and $\nu$. The original approximations are recovered for certain specials values of these two parameters. This offers a simple effective scheme for these and other relevant potentials in quantum mechanics.

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