Numerical Solutions for a Two-dimensional Quantum Dot Model View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-03-26

AUTHORS

F. Caruso, V. Oguri, F. Silveira

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. More... »

PAGES

1-6

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s13538-019-00656-7

DOI

http://dx.doi.org/10.1007/s13538-019-00656-7

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1113012102


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