Title: Contours of Contemporary Research: Perspectives Across Disciplines
Chief Editors: Dr. S. Durga, Dr. S. Sathyapriya, and Dr. V. A. Jane
ISBN: 978-81-17787-25-0
Chapter: 2
DOI: https://doi.org/10.59646/880/2
Authors: Anjali Rajput*, Kaushal Purohit, and Devansh Desai
Abstract
Quantum confinement modifies energy spectra, spatial localization, momentum distributions, and the response of matter to external perturbations. Information-theoretic quantities provide complementary descriptors of these changes beyond conventional observables such as eigen energies and transition frequencies. This chapter develops a unified treatment of Shannon entropy, Fisher information, Rényi and Tsallis entropies, statistical complexity, and quantum Fisher information in confined quantum systems. Starting from the Schrödinger equation and the density-operator formalism, it explains the physical interpretation, dimensional conventions, uncertainty relations, and computational evaluation of position- and momentum-space measures. Exactly solvable models, including the infinite quantum well and harmonic confinement, are used to expose scaling laws and analytic benchmarks; finite barriers, screened interactions, and magnetic confinement illustrate the need for numerical approaches. The discussion extends to quantum dots, coupled wells, low-dimensional heterostructures, molecular confinement, and quantum-enhanced sensing. Particular attention is paid to distinguishing classical Fisher information of a probability distribution from quantum Fisher information associated with parameter estimation. A reproducible workflow is proposed for numerical calculations, including normalization, Fourier transforms, convergence testing, and sensitivity analysis. The chapter concludes with current methodological limitations and research opportunities in open quantum systems, many-body confinement, external-field control, and physics-informed computation.
Keywords: quantum confinement; Shannon entropy; Fisher information; quantum Fisher information; Rényi entropy; Tsallis entropy; quantum dots; information-theoretic uncertainty; quantum sensing; external magnetic field.