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Wentzel-Kramers-Brillouin quantization rules for two-dimensional quantum dots
A SINHA, R ROYCHOUDHURY, Y P VARSHNI
Published in ELSEVIER SCIENCE BV
2003
Volume: 325
   
Pages: 214 - 223
Abstract
In this paper, we apply the semiclassical Wentzel-Kramers-Brillouin (WKB) approximation to an electron in a central force potential, confined in a two-dimensional disc, and we obtain the quantization rules for such a system. As explicit examples, we consider the two most widely studied potentials, viz., the parabolic potential (the harmonic oscillator) and the Hydrogenic impurity state (Coulomb potential) in two dimensions. Both the systems are confined within an impenetrable circular wall of radius r0. In particular, we determine the energies as well as eigenfunctions by this approach. On comparing these energies with those from exact numerical values, the agreement is found to be quite good. Moreover, the WKB approach is found to give a good estimate of the wave functions as well. These results suggest that the WKB approximation works well even for such rigid wall spatial confinement and the present approach can be applied to other confined systems such as those which are encountered in mesoscopic physics. © 2002 Elsevier Science B.V. All rights reserved.
About the journal
JournalData powered by TypesetPhysica B: Condensed Matter
PublisherData powered by TypesetELSEVIER SCIENCE BV
ISSN0921-4526