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

• Published in: International journal of quantum chemistry Vol. 124; no. 21
• Main Author: Banik, Sayan
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 05.11.2024; Wiley Subscription Services, Inc
• Subjects: Approximation; Entropy (Information theory); information entropies; Integrals; Mathematical analysis; Momentum; position and momentum space wave function; Quadratures; Quantum mechanics; Relativistic effects; Schrodinger equation; Schrödinger equation; Shannon scale functions; tanh‐sinh quadrature; Wave functions
• ISSN: 0020-7608; 1097-461X
• DOI: 10.1002/qua.27496

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. This work aims to develop a Shannon wavelet‐based scheme to approximate position and momentum space information entropies with reasonably less computational cost for non‐relativistic quantum mechanical models. The scheme, implemented in Python using Jupyter Notebook, has been tested for various exactly and quasi‐exactly solvable potentials in confined domains. Approximate entropy values are presented in tables, and the associated approximation errors are illustrated through graphical plots.