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

Abstract

We solve the Schrödinger 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 \( P = P_{r} P_{p} > 1 \).

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Ikot, A.N., Rampho, G.J., Amadi, P.O. et al. Shannon entropy and Fisher information-theoretic measures for Mobius square potential. Eur. Phys. J. Plus 135, 503 (2020). https://doi.org/10.1140/epjp/s13360-020-00525-2

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