Information‐Entropic Measures in Confined Isotropic Harmonic Oscillator. Issue 12 (13th September 2018) - Mukherjee, Neetik
Abstract: Information‐based uncertainty measures like Rényi entropy ( R ), Shannon entropy ( S ) and Onicescu energy ( E ) are employed to understand the influence of radial confinement in an isotropic harmonic oscillator (IHO). The transformation of the Hamiltonian into a dimensionless form gives an idea of the composite effect of oscillation frequency (ω) and confinement radius ( r c ). For a given quantum state, accurate results are provided by applying the respective exact analytical wave function in the r ‐space. The p ‐space wave functions are produced from Fourier transforms of radial functions. Pilot calculations are done taking order of entropic moments ( α, β ) as ( 3 5, 3 ) in r ‐ and p ‐spaces. A detailed, systematic analysis is performed for a 3D confined harmonic oscillator (CHO) with respect to state indices n r, l, and r c . It has been found that the CHO acts as a bridge between particles in a spherical box and the 3D free IHO. In the low‐ r c region, E r increases while R r α, S r decrease with the rise in n r . At moderate r c, there exists an interaction between two competing factors: i) radial confinement (localization) and ii) accumulation of radial nodes with growth of n r (delocalization). Most of these results are reported here for the first time, revealing many new interesting features. Abstract : Rényi and Shannon entropies, and Onicescu energy are employed to understand the influence of radial confinement in isotropic harmonic oscillators (IHOs). The Hamiltonian is transformed into a dimensionless form giving an idea of the composite effect of oscillation frequency (ω) and confinement radius ( r c ). The confined harmonic oscillator acts as a bridge between particles in a spherical box and the 3D free IHO.