Solving the two-dimensional Schrödinger equation using basis truncation: A hands-on review and a controversial case
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Solutions of the Schrödinger equation by spanning the wave function in a complete basis is a common practice in many-body interacting systems. We shall study the case of a two-dimensional quantum system composed of two interacting spinless electrons and see that the correctness of the matrix approach depends inexplicably on the type of interaction existing between particles. Also, we shall extend the present study to other systems of special interest in order to ilustrate the method.
KeywordMatrix mechanics quantum rings coupled harmonic oscillators
PACS Nos02.30.Mv 02.60.Dc 03.65.−w 03.65.Ge
J Batle acknowledges fruitful discussions with J Rosselló, Maria del Mar Batle and Regina Batle. J Batle also appreciates fruitful discussions with Pierre-Francois Loos. All authors appreciate the advice given by the anonymous referees.