Information entropy in excited states in confined quantum systems

Abstract: The present contribution constitutes a brief account of information theoretical analysis in several representative model as well as real quantum mechanical systems. There has been an overwhelming interest to study such measures in various quantum systems, as evidenced by a vast amount of publications in the literature that has taken place in recent years. However, while such works are numerous in so-called \emph{free} systems, there is a genuine lack of these in their constrained counterparts. With this in mind, this chapter will focus on some of the recent exciting progresses that has been witnessed in our laboratory \cite{sen06,roy14mpla,roy14mpla_manning,roy15ijqc, roy16ijqc, mukherjee15,mukherjee16,majumdar17,mukherjee18a,mukherjee18b,mukherjee18c,mukherjee18d,majumdar20,mukherjee21,majumdar21a, majumdar21b}, and elsewhere, with special emphasis on following prototypical systems, namely, (i) double well (DW) potential (symmetric and asymmetric) (ii) \emph{free}, as well as a \emph{confined hydrogen atom} (CHA) enclosed in a spherical impenetrable cavity (iii) a many-electron atom under similar enclosed environment.