arXiv subjects

H. E. Montgomery Jr

Publications and source records attributed to H. E. Montgomery Jr.

5 recordsLinked to original sources

arXiv2023

The confined helium atom; an Informational approach

In this work we study the helium atom confined in a spherical impenetrable cavity by using informational entropies. We use the variational method to obtain the energies and wave functions of the confined helium atom as a function of the cavity radius $r_0$. As trial wave functions we use one uncorrelated function and four functions with different degrees of electronic correlation. We computed the Shannon entropy, Fisher information, Kullback--Leibler entropy, Disequilibrium, Tsallis entropy and Fisher--Shannon complexity, as a function of the box radius $r_0$. We found that these entropic measures are sensitive to electronic correlation and can be used to measure it. These entropic measures are less sensitive to electron correlation in the strong confinement regime ($r_0<1$ a.u.).

quant-ph↗

arXiv2010

H2+ embedded in a Debye plasma: Electronic and vibrational properties

The effect of plasma screening on the electronic and vibrational properties of the H2+ molecular ion was analyzed within the Born-Oppenheimer approximation. When a molecule is embedded in a plasma, the plasma screens the electrostatic interactions. This screening is accounted for in the Schrödinger equation by replacing the Coulomb potentials with Yukawa potentials that incorporate the Debye length as a screening parameter. Variational expansions in confocal elliptical coordinates were used to calculate energies of the 1ssg and the 2psu states over a range of Debye lengths and bond distances. When the Debye length is comparable to the equilibrium bond distance, the plasma screening reshapes the potential energy curve. Expectation values, dipole polarizabilities and spectroscopic constants were calculated for the 1ssg state.

physics.plasm-ph↗

arXiv2010

Electron correlation energy in confined two-electron systems

Radial, angular and total correlation energies are calculated for four two-electron systems with atomic numbers Z=0-3 confined within an impenetrable sphere of radius R. We report accurate results for the non-relativistic, restricted Hartree-Fock and radial limit energies over a range of confinement radii from 0.05 - 10 a0. At small R, the correlation energies approach limiting values that are independent of Z while at intermediate R, systems with Z > 1 exhibit a characteristic maximum in the correlation energy resulting from an increase in the angular correlation energy which is offset by a decrease in the radial correlation energy.

physics.atom-ph↗

arXiv2009

Lower Bound for LMC complexity measure

Lower bound for the shape complexity measure of López-Ruiz-Mancini-Calbet (LMC), $C_{LMC}$, is derived. Analytical relations for simple examples of the harmonic oscillator, the hydrogen atom and two-electron 'entangled artificial' atom proposed by Moshinsky are derived. Several numerical examples of the spherically confined model systems are presented as the test cases. For the homogeneous potential, $C_{LMC}$ is found to be independent of the parameters in the potential which is not the case for the non-homogeneous potentials.

physics.chem-ph↗

arXiv2008

Exact solutions for the D-dimensional spherical isotropic confined harmonic oscillator

We study the size effect on the energy levels of the D-dimensional isotropic harmonic oscillator confined within a box of radius $r_c$ with impenetrable walls. Two different approaches are used to obtain the energy eigenvalues and eigenfunctions for D=1,2,...,5. In the first we solve the Schroedinger equation exactly. In the second we use a series expansion of the wave function. The numerical results obtained are extremely accurate; these values are reported with 50 decimal places.

math-ph↗