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Formula Method for Bound State Problems

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Abstract

We present a simple formula for finding bound state solution of any quantum wave equation which can be simplified to the form of \({\Psi''(s)+\frac{(k_1-k_2s)}{s(1-k_3s)} \Psi'(s)+\frac{(As^2+Bs+C)}{s^2(1-k_3s)^2} \Psi(s)=0}\). The two cases where k 3 = 0 and \({k_3\neq 0}\) are studied. We derive an expression for the energy spectrum and the wave function in terms of generalized hypergeometric functions \({_2F_1(\alpha,\,\beta;\,\gamma;\,k_3s)}\). In order to show the accuracy of this proposed formula, we resort to obtaining bound state solutions for some existing eigenvalue problems in a rather more simplified way. This method has shown to be accurate, efficient, reliable and very easy to use particularly when applied to vast number of quantum potential models.

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Authors and Affiliations

  1. Applied Theoretical Physics Division, Department of Physics, Federal University Lafia, P. M. B. 146, Lafia, Nigeria

    B. J. Falaye

  2. Department of Physics, Faculty of Science, An-Najah National University, New Campus, P. O. Box 7, Nablus, West Bank, Palestine

    S. M. Ikhdair

  3. Department of Physics, University of Zanjan, Zanjan, Iran

    M. Hamzavi

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  1. B. J. Falaye
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  3. M. Hamzavi
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Falaye, B.J., Ikhdair, S.M. & Hamzavi, M. Formula Method for Bound State Problems. Few-Body Syst 56, 63–78 (2015). https://doi.org/10.1007/s00601-014-0937-9

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