Variational quantum Monte Carlo for the harmonium system

Abstract

Relatively good accuracy (< 2%) for intermediate and strong regime for the ground state energy of the harmonium system (Hook's atom) was obtained by variational Monte-Carlo (VMC) calculations. Our study focus on the variation of the ground state energy with respect to the oscillation frequency ω and the balance between the three different part of the energy (kinetic, coulomb and harmonic). Results were compared with several exactly known values of ground state energy for a series of discreet but limited values of the oscillation frequency.