English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we obtain approximate bound state solutions of $N$-dimensionaltime independent fractional Schr\"{o}dinger equation for generalisedpseudoharmonic potential which has the form$V(r^{\alpha})=a_1r^{2\alpha}+\frac{a_2}{r^{2\alpha}}+a_3$. Here$\alpha(0<\alpha<1)$ acts like a fractional parameter for the space variable$r$. The entire study is composed with the Jumarie type derivative and theelegance of Laplace transform. As a result we successfully able to express theapproximate bound state solution in terms of Mittag-Leffler function andfractionally defined confluent hypergeometric function. Our study may betreated as a generalization of all previous works carried out on this topicwhen $\alpha=1$ and $N$ arbitrary. We provide numerical result of energyeigenvalues and eigenfunctions for a typical diatomic molecule for different$\alpha$ close to unity. Finally, we try to correlate our work with Cornellpotential model which corresponds to $\alpha=\frac{1}{2}$ with $a_3=0$ andpredict the approximate mass spectra of quarkonia.

Higher dimensional fractional time independent Schr\"{o}dinger equation via Jumarie fractional derivative with generalized pseudoharmonic potential