Fourier transform technique in variational treatment of two-electron parabolic quantum dot
S. Şakiroĝlua)†, A. Yildiza), Ü. Doĝana), K. Akgüngöra), H. Epika), Y. Ergünb), H. Saric) and ì. Sökmena)
a Physics Department, Dokuz Eylül University, Buca -?zmir 35160, Turkey; b Physics Department, Anadolu University, Eski?ehir 26470, Turkey; c Physics Department, Cumhuriyet University, Sivas 58140, Turkey
Abstract In this work, we propose an efficient method of reducing the computational effort of variational calculation with a Hylleraas-like trial wavefunction. The method consists of introducing integral transforms for the terms as $r_{12}^k\exp(-\lambda r_{12})$ which provide the calculation of the expectation value of energy and the relevant matrix elements to be done analytically over single-electron coordinates instead of Hylleraas coordinates. We have used this method to calculate the ground state energy of a two-electron system in a spherical dot and a disk-like quantum dot separately. Under parabolic confinement potential and within effective mass approximation size and shape effects of quantum dots on the ground state energy of two electrons have been investigated. The calculation shows that our results even with a small number of basis states are in good agreement with previous theoretical results.
Received: 05 December 2008
Revised: 04 February 2009
Accepted manuscript online:
(Fermi surface: calculations and measurements; effective mass, g factor)
Fund: Project supported by the Cumhuriyet
University, National MOVPE Crystal Growth and Characterization
Laboratory, Turkey, DPT-K 120, TUBITAK (Grant Nos TBAG 105T492, TBAG
107T012, and TBAG-108T015).
Cite this article:
S. Şakiroĝlu, A. Yildiz, ü. Doĝan, K. Akgüngör, H. Epik, Y. Ergün, H. Sari and ì. Sökmen Fourier transform technique in variational treatment of two-electron parabolic quantum dot 2009 Chin. Phys. B 18 3508
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