ABSTRACT:The model of the confined hydrogen atom (CHA) was developed by Michels et al. [1] in the mid-1930s to study matter subject to extreme pressure. However, since the eigenvalues cannot be obtained analytically, even the most accurate calculations have yielded little more than 10 figure accuracy. In this work, we show that it is possible to obtain the CHA eigenvalues with extremely high accuracy (up to 100 decimal digits) and we do that using two completely different methods. The first is based on formal solution of the confluent hypergeometric function while the second uses a series method. We also compare radial expectation values obtained by both methods and conclude that the wave functions obtained by these two different approaches are of high quality. In addition, we compute the hyperfine splitting constant, magnetic screening constant, polarizability in the Kirkwood approximation, and pressure as a function of the box radius.

No abstract

No abstract

In a recent work, Al-Jaber (2008 Int. J. Theor. Phys. 47 1853) calculated the energy eigenvalues of a confined N-dimensional harmonic oscillator. He also examined the correlation between the energy eigenvalues of harmonic oscillators in different dimensions. In the present work, we improve the energy eigenvalues obtained by Al-Jaber. In particular, we study the size effects on the energies of the ground and a few excited states of the N-dimensional (N=1–5 and N=10), isotropic harmonic oscillator confined within an impenetrable hypersphere of radius rc. The numerical results obtained are the most accurate reported to date, with the ground state values reported to 50 decimal places. Our eigenvalues are compared to those published previously. As a counterpart to Al-Jaber's work, we also report radial expectation values, dipole transition moments and dipole polarizabilities for N=1–3 as a function of rc.

ABSTRACT:A study of the two-dimensional hydrogen atom confined within a circle of impenetrable walls is presented. The potential inside the box is Coulomb type, whereas outside it is infinite. The energy eigenvalues and some radial wave function properties are computed with high accuracy for different box sizes. We derive the polarizability in the Kirkwood approximation, calculate the Fermi contact term as a function of the confinement radius, and investigate the filling order of the one-electron states. When the electronic configuration of many electrons is constructed by means of the Aufbau principle, the model predicts the inversion 2s-3d levels in the N atom.