Accurate wavefunctions for the confined hydrogen atom at high pressures

Abstract

Wavefunctions are proposed for the 1s, 2p and 3d states of the compressed hydrogen atom at high pressures. It is shown that these wavefunctions give highly accurate energies in the positive energy region.

Energy Spectra of tightly Confined Systems

“…Therefore using Equation (30) and Equation (43), we obtain < >= 105.1535 Hartrees, which is equivalent to 201.3070 Ry. The corresponding exact value is 937.986 Ry (Varshni, 1997). The difference between the two results indicates that the intermediate region should be considered more carefully, which will be our proposal of future work.…”

Scaling Relation For The Energy Levels Of A Hydrogen Atom At High Pressures

“…Such a plot is shown in Figure 1. The data for the 1s, 2p, and 3d levels are from [18] and [20]. For the 4f level, fresh calculations for exact values of the energy were carried out by the author.…”

The hydrogen atom confined in both Debye screening potential and impenetrable spherical box

“…For example, some papers have discussed the importance of Debye screening in astrophysical plasma diagnostics, astrophysical observations, and calculating partition functions in thermodynamics. Other papers have discussed the applications in astrophysical phenomena like the mass radius relation in the theory of white dwarfs and in the determination of the rate of escape of stars from galactic and globular clusters [30][31][32]. Studies into the properties of an atom confined in the impenetrable spherical box have also received much attention since in 1937, Michels et al proposed a model to study the variation of a static dipole under the effective pressure acting on the surface [33].…”