Analysis of asymmetric confined quantum systems by the direct variational method

Abstract

The variational method is used to calculate the ground state energy of the hydrogen atom confined within hard spherical and cylindrical surfaces, for an atomic nucleus which is off the center of symmetry of the confining boundary. It is shown that the wave function for the free hydrogen atom in spherical coordinates (referred to the center of symmetry of the confining geometry) can be used without further assumptions to construct the trial wave function systematically. The latter is assumed to be the product of the free wave function and a simple cutoff function that satisfies the appropriate boundary conditions. We compute the ground state energy for these systems and the results are in good agreement with more sophisticated calculations, thus proving the reliability of the proposed strategy.

Integral evaluation in the case of a helium atom positioned off-center in a spherical box

“…This is consistent with the rew x sults of a hydrogen atom as reported in Ref. 11 . Addition of the p -type orbital has the most proz nounced effect on energy when the displacement is around 50% of the sphere radius.…”

Electronic confinement effects on the reaction field type calculations of solvent effects

“…There are a variety of methods for the quantitative study of the energy of atoms in boxes. They span from the exact resolution of the Schrödinger equation in some favorable cases to perturbative theories, also including the variational method, which has become a very useful tool for researching systems constrained in boxes with different symmetries . For example, research has been carried out in the helium atom within a spherical box, with the intention of modeling the effect of pressure in atoms with more than one electron .…”

Density dynamics in some quantum systems

“…[201] The physical properties of confined atoms as well as confined molecules depend on the confinement volume. [202][203][204][205][206][207] There have been wide applications of confined quantum systems such as in physics, chemistry, and biology. [201,[208][209][210][211][212] The models of confined quantum systems such as confined atoms and confined molecules have been used to study matters under high pressure.…”