Twoelectron quantum dot model revisited: bound states and other analytical and numerical solutions
Abstract
The model of a twoelectron 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 $1/r$ and $\ln r$ Coulombianlike 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 $l=0$ is predicted and the respective eigenvalues are determined.
 Publication:

arXiv eprints
 Pub Date:
 August 2016
 arXiv:
 arXiv:1608.04375
 Bibcode:
 2016arXiv160804375C
 Keywords:

 Quantum Physics
 EPrint:
 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