Analytical approximate bound state solution of Schrödinger equation in $D$-dimensions with a new mixed class of potential for arbitrary $\ell$-state via asymptotic iteration method

Tapas Das

doi:10.1016/j.cjph.2016.10.001

paper

Analytical approximate bound state solution of Schrödinger equation in $D$ -dimensions with a new mixed class of potential for arbitrary $ℓ$ -state via asymptotic iteration method

arXiv:1610.04225 · doi:10.1016/j.cjph.2016.10.001

Abstract

The bound state solutions of the $D$ -dimensional Schrödinger equation for new mixed class of potential, $V (r) = \frac{V _{1}}{r ^{2}} + \frac{V _{2} e ^{- α r}}{r} + V_{3} co t h α r + V_{4},$ are studied within the framework of the Pekeris approximation for any arbitrary $ℓ$ -state. Asymptotic iteration method (AIM) is used for the work. The energy spectrum are obtained as well as their corresponding normalized eigenfunctions are derived in terms of generalized hypergeometric functions $_{2} F_{1} (a, b, c; z)$ . It is shown that using the Pekeris approximation, present potential model is very much capable of deriving other well known potentials quite easily and corresponding solutions are in excellent agreement with the previous work carried out in literature.

arXiv comment18 Pages, 57 References, No figure and table, Chinese Journal of Physics (2016)

Analytical approximate bound state solution of Schrödinger equation in D-dimensions with a new mixed class of potential for arbitrary ℓ-state via asymptotic iteration method

Abstract

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Analytical approximate bound state solution of Schrödinger equation in $D$ -dimensions with a new mixed class of potential for arbitrary $ℓ$ -state via asymptotic iteration method