Information theoretic measures within Schr\"odinger-Dunkl framework in spherical coordinates

TL;DR

This paper analytically solves the Schr"odinger-Dunkl equation with Deng-Fan potential in spherical coordinates, calculating various information-theoretic measures and demonstrating the effects of reflection operators on wave functions and statistical measures.

Contribution

It introduces an analytical approach to the Schr"odinger-Dunkl equation with Deng-Fan potential, including new approximations and detailed information-theoretic analysis.

Findings

High accuracy (within 0.0001%) between analytical and numerical results.

Effect of reflection operators on wave functions and information measures.

Comprehensive statistical analysis of Deng-Fan potential in Dunkl framework.

Abstract

In this article, we have presented analytical solution of Schr\"odinger-Dunkl equation with Deng-Fan molecular potential in spherical coordinates. The ro-vibrational energy of some selected diatomic molecules ScH, TiH, VH and CrH are obtained under a simple, new approximation to the centrifugal term in presence of three reflection operators and Dunkl parameters. The angular wave functions are obtained in terms of Jacobi polynomial, whereas radial wave functions in terms of hypergeometric function. The analytical results of Shannon entropy, expectation, Heisenberg uncertainty, entropic moment, disequilibrium, R\'enyi entropy and Tsallis entropy of marginal density (radial r, and angular {\theta}, {\phi}) and total density functions are obtained in Schr\"odinger-Dunkl system with respect to the weighted Lebesgue measure. This has been possible by making use of factorization method for Shannon entropy. The absolute per cent deviation between the analytical and numerical results for all the information theoretic measures remain well within 0.0001%. The effect of reflection operators on angular wave solutions and on information theoretic measures are shown. In essence, a number of statistical measures have been reported for Deng-Fan potential in the Dunkl-Schr\"odinger framework.