Shannon entropy and Fisher information-theoretic measures for Mobius square potential

We solve the Schrodinger equation for the Mobius square potential using the newly proposed Nikiforov-Uvarov functional analysis method. The approximate energy spectrum and unnormalized wave function are obtained in a closed form. The Shannon entropy, Fisher information, Fisher-Shannon product and the expectation values for the Mobius square are investigated in position and momentum space for the low lying states corresponding to n = 0 and 1. All the theoretic information theories investigated satisfied their corresponding inequality such as Bialynicki-Birula-Mycielski, Stam-Cramer-Rao inequalities and the Fisher-Shannon product relation P = PrPp > 1.