Soft and hard confinement of a two-electron quantum system
Richard L. Hall, Nasser Saad, K. D. Sen
TL;DR
This paper investigates a two-electron quantum system under soft and hard confinement, providing exact solutions for special cases and highly accurate numerical results for general scenarios, with discussions on degeneracy.
Contribution
It introduces exact analytical solutions for specific parameters and high-precision numerical solutions for the general case of a confined two-electron system.
Findings
Exact solutions for special parameter sets
High-precision numerical solutions (18 decimal places)
Discussion on degeneracy in confined systems
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 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.
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