Energy and information analysis for confined H atom in harmonic environment

Abstract

Over the past two decades, constrained quantum systems have arisen to be a field of considerable importance in physical, chemical and biological sciences. In this work, we have investigated the behavior of a confined H atom inside a harmonic environment: . The eigenvalue equation is solved using a generalized Legendre pseudospectral method, which offers an optimal, non-uniform spatial discretization. By means of a symmetrization technique and a non-linear mapping, a symmetric eigenvalue equation is obtained. A detailed energy analysis reveals that (a) for all the states, energy values decrease with growth in confinement radius, rc (b) for fixed number of nodes, it grows with rise in l, and (c) at a fixed n, it decreases with progress in l. Interestingly, the energy arrangement of various quantum states is found to be very different from that in a free H atom. A general rule has been proposed to understand the energy ordering pattern. Furthermore, we have analyzed some information-based quantities like Shannon information entropy, Fisher information and Onicescu energy, in position and momentum spaces for this soft, impenetrable stressed system. These are examined with respect to rc as well as n, l quantum numbers. Additionally, the Compton profile and Compton entropy have also been explored here.