A quantum Monte Carlo study of confined quantum systems: application to harmonic oscillator and hydrogenic-like atoms

Abstract

The correlation function quantum Monte Carlo (CFQMC) approach is employed to study the energy spectra of confined quantum systems. This method, applied originally to determine rovibrational eigenenergies of molecules, is utilized here to calculate the energy levels of hydrogen atom, helium cation, lithium dication and two confined harmonic oscillator (HO) models: the one-dimensional HO within a box of impenetrable walls and the three-dimensional one confined by an impenetrable spherical box. The dependence of the eigenenergies on functional form and the number of the basis functions are analyzed for various confinement parameters. The present results are compared with those previously published, and the efficiency of the CFQMC method to treat confined quantum systems is discussed.

Coulomb correlation and information entropies in confined helium-like atoms

“…Some of the main aspects of the strong or extreme confinement regime is the fact that, in this region, the effects of electronic correlation become essentially null, however the influence of the confining potential becomes greater than Coulomb potential. In this specific region, the system have the probability density highly concentrated in position space [82,83]. These characteristics are obtained in the present work through an elegant informational analysis.…”

Shannon entropy: A study of confined hydrogenic-like atoms

“…A particularly interesting situation is when the confinement is rigorous (strong confinement regime). For example, it was shown that in such regime the energies of confined hydrogenic-like atoms tends to the values of a particle confined in a spherical cage [32]. Recent studies for the harmonic potential showed that such analysis can be made based on Shannon entropy [33,34].…”

“…A particularly interesting situation is when the confinement is rigorous (strong confinement regime). For example, it was shown that in such regime the energies of confined hydrogenic-like atoms tends to the values of a particle confined in a spherical cage [32]. Recent studies for the harmonic potential showed that such analysis can be made based on Shannon entropy [33,34].The entropy sum (S t ), quantity defined as the sum of the Shannon entropies in the position and momentum spaces, has occupied a privileged place in the study of quantum systems in the information theory context.…”

Confinement effects on the electronic structure of M-shell atoms: A study with explicitly correlated wave functions

“…The radial orbitals and the C k coefficients of the model function, Equation , and the c k parameters of the correlation function, Equation , are optimized for each term and confinement radius. It is worth mentioning here a recent calculation of excited states of confined single‐particle systems employing the correlation function quantum Monte Carlo method that combines the use of basis function and the Variational Monte Carlo.…”