Soluções numéricas e analíticas de um modelo de quantum dot com dois elétrons (original) (raw)

The main scope of this work is to search numerical an analytical solutions for the Schrödinger equation that describes a two electron quantum dot. Once confi rmed that both methods are in agreement with the results for the same parameters new forms of the potential energy were considered in order to try to clarify the real form of the Coulombian potential for the quantum dot in two spatial dimensions. The Coloumbian term of the potential energy in a strictly two-dimensional space is given by ln r (in atomic units) but in the literature the term is usually considered strictly in its three-dimensional form 1=r. This monograph provides numerical results for both potentials which can be further compared with experimental data to prove the actual shape of the potential energy of a quantum dot. The numerical method also allows the determination of new bound states in negative energy regions for the case when the angular momentum quantum number is l = 0.