Shannon Wavelet-Based Approximation Scheme for Information Entropy Integrals in Confined Domain

Abstract

In this work, the author attempted to develop a Shannon wavelet-based numerical scheme to approximate the information entropies in both configuration and momentum space corresponding to the ground and adjacent excited energy states of one-dimensional Schrödinger equation appearing in non-relativistic quantum mechanics. The development of this scheme is based on the judicious use of sinc scale functions as an approximation basis and a suitable numerical quadrature to approximate entropies in position and momentum spaces. Priori and posteriori errors appearing in the approximations of wave functions and entropy integrals have been discussed. The scheme (coded in Python) has been subsequently exercised for various exactly solvable and quasi-exactly solvable non-relativistic quantum mechanical models in confined domain.