Solving a two-electron quantum dot model in terms of polynomial solutions of a Biconfluent Heun equation |
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Authors: | F Caruso J Martins V Oguri |
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Institution: | 1. Centro Brasileiro de Pesquisas Físicas - Rua Dr. Xavier Sigaud, 150, 22290-180, Urca, Rio de Janeiro, RJ, Brazil;2. Instituto de Física Armando Dias Tavares, Universidade do Estado do Rio de Janeiro - Rua São Francisco Xavier, 524, 20550-900, Maracanã, Rio de Janeiro, RJ, Brazil |
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Abstract: | The effects on the non-relativistic dynamics of a system compound by two electrons interacting by a Coulomb potential and with an external harmonic oscillator potential, confined to move in a two dimensional Euclidean space, are investigated. In particular, it is shown that it is possible to determine exactly and in a closed form a finite portion of the energy spectrum and the associated eigenfunctions for the Schrödinger equation describing the relative motion of the electrons, by putting it into the form of a biconfluent Heun equation. In the same framework, another set of solutions of this type can be straightforwardly obtained for the case when the two electrons are submitted also to an external constant magnetic field. |
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Keywords: | Schrö dinger equation Harmonic oscillator potential Two-electron system Quantum dot model |
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