An analytical treatment of the energy spectrum of hydrogen-like atoms perturbed by a generalized van der Waals potential

Abstract

Hydrogen-like atoms are two-particle systems governed with spherically symmetric potentials, their nonrelativistic Schrödinger equations can be solved analytically yielding exact information about their spectra. Vigorous interest in the investigation of their behavior under the influence of external fields has been increased over the years. The main goal of the present work is to investigate the effect of a generalized van der Waals potential on the energy spectra of the hydrogen-like atoms. Our treatment is based on the Oscillator Representation Method (ORM). The energy spectrum is studied for various parameters over an atom-surface distance 50nm-300nm for different hydrogen-like atoms, like H, He + , Li 2+ , Be 3+ , B 4+ , etc.

Two-electron quantum dot in a magnetic field: Analytic solution for finite potential model

“…The transition magnetic field value obtained for the Gaussian potential is closer to the experimental value indicating that indeed the discrepancy may be at least partly due to the infinite harmonic potential assumption by Wagner et al [32] developed the oscillator representation method (ORM) arising from ideas and methods of the quantum field theory. Using the ORM the binding energies of a number of systems with various types of potentials including the Coulomb and power-law potentials, exponentially screened Coulomb potential, logarithmic potential [32,33], van der Waals potential [34], cavity model [35], and a two-electron quantum dot in a magnetic field [36] have been calculated. The ORM results agree very well with the results obtained by variational numerical methods and analytic methods for these potentials.…”