A computational scheme for solving elliptic boundary value problems with axially symmetric confining potentials using different sets of one-parameter basis functions is presented. The efficiency of the proposed symbolic-numerical algorithms implemented in Maple is shown by examples of spheroidal quantum dot models, for which energy spectra and eigenfunctions versus the spheroid aspect ratio were calculated within the conventional effective mass approximation. Critical values of the aspect ratio, at which the discrete spectrum of models with finite-wall potentials is transformed into a continuous one in strong dimensional quantization regime, were revealed using the exact and adiabatic classifications. © 2010 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Gusev, A. A., Chuluunbaatar, O., Gerdt, V. P., Rostovtsev, V. A., Vinitsky, S. I., Derbov, V. L., & Serov, V. V. (2010). Symbolic-numeric algorithms for computer analysis of spheroidal quantum dot models. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6244 LNCS, pp. 106–122). https://doi.org/10.1007/978-3-642-15274-0_10
Mendeley helps you to discover research relevant for your work.