Two-electron quantum dot model revisited: bound states and other analytical and numerical solutions. (arXiv:1608.04375v2 [quant-ph] UPDATED)

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 $1/r$ and $\ln r$
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 $l=0$ is predicted and the respective eigenvalues are
determined.

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