Information theoretic measures of isotropic Dunkl oscillator in spherical coordinates

An information theoretic analysis is done for the isotropic harmonic oscillator potential within the Dunkl-Schr\"odinger framework in spherical coordinates. Starting from the exact analytical eigensolution, various quantum information measures such as Shannon entropy, R\'enyi information, Tsallis entropy are derived. Besides, their relative measures like relative Shannon, relative R\'enyi, relative Tsallis as well as corresponding divergences (Jensen-Shannon, Jensen-R\'enyi, Jensen-Tsallis) are also obtained. In order to get Shannon entropy, a novel factorization method is introduced. This is facilitated through the use of well-known weighted Lebesgue measure. The results from the Dunkl case agree exactly with the non-Dunkl scenario, when Dunkl parameters vanish. The reflection operators and Dunkl parameters considerably influence the above measures. These are portrayed in graphical forms.