ABSTRACT
Inequality constitutes the basis of the variational method for the approximate calculation of the ground state energy and the wave function. It consists of evaluating the expectation value of the Hamiltonian using a trial wave function Ψ which contains a number of variational parameters. These parameters are determined by minimizing the energy of this trial state. Apparently, a successful implementation of the variational principle relies highly on the choice of the trial wave function. The half-harmonic oscillator Hamiltonian can be diagonalized using the same approach as for solving the ordinary harmonic oscillator. An inherent feature of a many-electron system that should be considered is the screening effect of the negative charge cloud of an electron, which can effectively reduce the positive charge of the nucleon that acts on the other electron.
