Soft and hard confinement of a two-electron quantum system

Abstract

A model physical problem is studied in which a system of two electrons is subject either to soft confinement by means of attractive oscillator potentials or by entrapment within an impenetrable spherical box of finite radius $R.$ When hard confinement is present the oscillators can be switched off. Exact analytical solutions are found for special parameter sets, and highly accurate numerical solutions (18 decimal places) are obtained for general cases. Some interesting degeneracy questions are discussed at length.

17 pages, two figures. arXiv admin note: substantial text overlap with arXiv:1108.4878

References in corpus (6)

• Asymptotic iteration method for eigenvalue problems
• Criterion for polynomial solutions to a class of linear differential equation of second order
• Physical applications of second-order linear differential equations that admit polynomial solutions
• Effects of screened Coulomb impurities on autoionizing two-electron resonances in spherical quantum dots
• Dirac Equation with Spin Symmetry for the Modified Pöschl-Teller Potential in $D$-dimensions
• Discrete spectra for confined and unconfined -a/r + b r^2 potentials in d dimensions

Cited by in corpus (2)

• The Asymptotic Iteration Method Revisited
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