Two-electron quantum dot model revisited: bound states and other analytical and numerical solutions
Abstract
The model of a two-electron quantum dot, confined to move in a two dimensional flat space, is revisited. Generally, it is argued that the solutions of this model obtained by solving a biconfluent Heun equation have some limitations. In particular, some corrections are also made in previous theoretical calculations. The corrected polynomial solutions are confronted with numerical calculations based on the Numerov method, in a good agreement between both. Then, new solutions considering the and Coulombian-like potentials in (1+2)D, not yet obtained, are discussed numerically. In particular, we are able to calculate the quantum dot eigenfunctions for a much larger spectrum of external harmonic frequencies as compared to previous results. Also the existence of bound states for such planar system in the case is predicted and the respective eigenvalues are determined.
Keywords
Cite
@article{arxiv.1608.04375,
title = {Two-electron quantum dot model revisited: bound states and other analytical and numerical solutions},
author = {Francisco Caruso and Vitor Oguri and Felipe Silveira},
journal= {arXiv preprint arXiv:1608.04375},
year = {2019}
}
Comments
14 pages, 6 figures There is an error in Section 4: Numerical solutions for the $\ln r$ potential. In particular, the values shown in Table 4 and the plot of figure 5 are wrong