• Higher-dimensional fractional time-independent Schrödinger equation via fractional derivative with generalised pseudoharmonic potential

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      https://www.ias.ac.in/article/fulltext/pram/093/05/0076

    • Keywords

       

      Fractional radial Schrödinger equation; generalised pseudoharmonic potential; bound-state solutions; Mittag–Leffler function

    • Abstract

       

      In this paper, we obtain approximate bound-state solutions of $N$-dimensional time-independent fractional Schrödinger equation for the generalised pseudoharmonic potential which has the form $V(r^{\alpha}) = a_{1}r^{2\alpha} + (a_{2}/r^{2\alpha}) + a_{3}$. Here $\alpha$ (0 < $\alpha$ < 1) acts like a fractional parameter for the space variable $r$. The entire study consists of the Jumarie-type fractional derivative and the elegance of Laplace transform. As a result, we can successfully express the approximate bound-state solution in terms of Mittag–Leffler function and fractionally defined confluent hypergeometric function. Our study may be treated as a generalisation of all previous workscarried out on this topic when $\alpha = 1$ and $N$ arbitrary. We provide numerical result of energy eigenvalues and eigenfunctions for a typical diatomic molecule for different α close to unity. Finally, we try to correlate our work with a Cornell potential model which corresponds to $\alpha = 1/2$ with $a_{3} = 0$ and predicts the approximate mass spectra of quarkonia.

    • Author Affiliations

       

      TAPAS DAS1 UTTAM GHOSH2 SUSMITA SARKAR2 SHANTANU DAS3

      1. Kodalia Prasanna Banga High School (HS), South 24 Parganas, Kolkata 700 146, India
      2. Department of Applied Mathematics, University of Calcutta, Kolkata 700 073, India
      3. Reactor Control System Design Section (E & I Group), Bhabha Atomic Research Centre,Mumbai 400 085, India
    • Dates

       
  • Pramana – Journal of Physics | News

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