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

摘要

The bound state solutions of the $D$-dimensional Schr\"{o}dinger equation fornew mixed class of potential, $V(r)=\frac{V_1}{r^2}+\frac{V_2e^{-\alphar}}{r}+V_3coth\alpha r+V_4\,,$ are studied within the framework of the Pekerisapproximation for any arbitrary $\ell$-state. Asymptotic iteration method (AIM)is used for the work. The energy spectrum are obtained as well as theircorresponding normalized eigenfunctions are derived in terms of generalizedhypergeometric functions $\,_{2}F_{1}(a,b,c;z)$. It is shown that using thePekeris approximation, present potential model is very much capable of derivingother well known potentials quite easily and corresponding solutions are inexcellent agreement with the previous work carried out in literature.