中国物理B ›› 2009, Vol. 18 ›› Issue (8): 3508-3516.doi: 10.1088/1674-1056/18/8/062

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Fourier transform technique in variational treatment of two-electron parabolic quantum dot

Y. Ergün1, H. Sar12, S. ?akiro?lu3, A. Y1ld1z3, Ü. Do?an3, K. Akgüng?r3, H. Epik3, ?. S?kmen3   

  1. (1)Physics Department, Anadolu University, Eski?ehir 26470, Turkey; (2)Physics Department, Cumhuriyet University, Sivas 58140, Turkey; (3)Physics Department, Dokuz Eylül University,Buca -?zmir 35160, Turkey
  • 收稿日期:2008-12-05 修回日期:2009-02-04 出版日期:2009-08-20 发布日期:2009-08-20
  • 基金资助:
    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).

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)   

  1. 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
  • Received:2008-12-05 Revised:2009-02-04 Online:2009-08-20 Published:2009-08-20
  • Supported by:
    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).

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摘要： 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 r12^k\exp(-λ r12) 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.

关键词: two-electron quantum dot, parabolic confinement, variational method, Hylleraas coordinates

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.

Key words: two-electron quantum dot, parabolic confinement, variational method, Hylleraas coordinates

中图分类号:  (Quantum dots)

  • 73.21.La
71.18.+y (Fermi surface: calculations and measurements; effective mass, g factor)