Information theoretic measures in one-dimensional Dunkl oscillator

Abstract

We consider the solution of one dimensional Schrödinger Dunkl equation for energies and eigenfunctions. Then we provide analytical expressions for various information theoretic measures. For a given density function, quantities such as position expectation value, entropic moment, disequilibrium, Rényi entropy, Shannon entropy, Tsallis entropy, Fisher information are presented. Next, a few relative information measures corresponding to two density functions, like relative entropy, relative Fisher, relative Rényi, relative Tsallis, along with their associated Jensen divergences such as Jensen–Shannon divergence, Jensen–Fisher divergence, Jensen–Rényi divergence, Jensen–Tsallis divergence are treated. Sample results are provided in graphical form. Dependence of these quantities on the Dunkl parameter μ shows distinct features for μ < 0 and μ > 0.