Fisher information in confined isotropic harmonic oscillator

Abstract

Fisher information ($I$) is investigated in a confined harmonic oscillator (CHO) enclosed in a spherical enclosure, in conjugate $r$ and $p$ spaces. A comparative study between CHO and a free quantum particle in spherical box (PISB), as well as CHO and respective free harmonic oscillator (FHO) is pursued with respect to energy spectrum and $I$. This reveals that, a CHO offers two exactly solvable limits, namely, a PISB and an FHO. Moreover, the dependence of $I$ on quantum numbers $n_{r}, l, m$ in FHO and CHO are analogous. The role of force constant is discussed. Further, a thorough systematic analysis of $I$ with respect to variation of confinement radius $r_c$ is presented, with particular attention on \emph{non-zero}-$(l,m)$ states. Considerable new important observations are recorded. The results are quite accurate and most of these are presented for the first time.