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Energy and information-entropic measures of Hulthén potential in D dimension by a new approximation to centrifugal term

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Abstract

Energy spectrum as well as various information theoretic measures are considered for Hulthén potential in D dimension. For a given \(\ell \ne 0\) state, approximate closed expressions are derived, following a simple intuitive approximation for accurate representation of centrifugal term. This is derived from a linear combination of two widely used Greene–Aldrich and Pekeris-type approximations. Energy, wave function, normalization constant, expectation value in r and p space, Heisenberg uncertainty relation, entropic moment of order \({\bar{\alpha }}\), Shannon entropy, Rényi entropy, disequilibrium, majorization as well as four selected complexity measures like LMC (López-Ruiz, Mancini, Calbert), shape Rényi complexity, Generalized Rényi complexity and Rényi complexity ratio are offered for different screening parameters (\(\delta \)). The effective potential is described quite satisfactorily throughout the whole domain. Obtained results are compared with theoretical energies available in literature, which shows excellent agreement. Performance of six different approximations to centrifugal term is critically discussed. An approximate analytical expression for critical screening for a specific state in arbitrary dimension is offered. Additionally, some inter-dimensional degeneracy occurring in two states, at different dimension for a particular \(\delta \) is also uncovered.

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Acknowledgements

AKR gratefully acknowledges financial support from MATRICS, DST-SERB, New Delhi (Sanction Order MTR/2019/000012) and partial assistance from DST-SERB (Sanction Order CRG/2019/000293) is appreciated. We thank the two anonymous referees for their valuable suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Vivekananda College, Kolkata, West Bengal, 700063, India

    Debraj Nath

  2. Department of Chemical Sciences, Indian Institute of Science Education and Research (IISER) Kolkata, Mohanpur, Nadia, Kolkata, 741246, West Bengal, India

    Amlan K. Roy

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  1. Debraj Nath
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  2. Amlan K. Roy
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DN: Conceptualization, Investigation, Methodology, Writing-original draft. AKR: Conceptualization, Investigation, Methodology, Writing-original draft.

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Correspondence to Debraj Nath or Amlan K. Roy.

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Nath, D., Roy, A.K. Energy and information-entropic measures of Hulthén potential in D dimension by a new approximation to centrifugal term. J Math Chem 61, 835–858 (2023). https://doi.org/10.1007/s10910-022-01440-w

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