Numerical solutions for a two dimensional quantum dot model
arXiv:1903.06707 · doi:10.1007/s13538-019-00656-7
Abstract
In this paper, a quantum dot mathematical model based on a two-dimensional Schrödinger equation assuming the 1/r inter-electronic potential is revisited. Generally, it is argued that the solutions of this model obtained by solving a biconfluent Heun equation have some limitations. The known polynomial solutions are confronted with new numerical calculations based on the Numerov method. A good qualitative agreement between them emerges. The numerical method being more general gives rise to new solutions. In particular, we are now 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 state for such planar system, in the case l=0, is predicted and its respective eigenvalue is determined.
9 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1608.04375. We requested the withdrawal of this paper arXiv:1608.04375