Ground state energy of excitons in quantum dot treated variationally via Hylleraas-like wavefunction
S. Şakiroĝlua)†, ü. Doĝana), A. Yildiza), K. Akgüngöra), H. Epika), Y. Ergünb), H. Saric), and ì. Sökmena)
a Physics Department, Dokuz Eyl¨ul University, ˙Izmir 35160, Turkey; b Physics Department, Anadolu University, Eski¸sehir 26470, Turkey; c Physics Department, Cumhuriyet University, Sivas 58140, Turkey
AbstractIn this work, the effects of quantum confinement on the ground state energy of a correlated electron--hole pair in a spherical and in a disc-like quantum dot have been investigated as a function of quantum dot size. Under parabolic confinement potential and within effective mass approximation Ritz's variational method is applied to Hylleraas-like trial wavefunction. An efficient method for reducing the main effort of the calculation of terms like $r^k_{\rm eh}\exp(-\lambda r_{\rm eh})$ is introduced. The main contribution of the present work is the introduction of integral transforms which provide the calculation of expectation value of energy and the related matrix elements to be done analytically over single-particle coordinates instead of Hylleraas coordinates.
Received: 23 July 2008
Revised: 27 October 2008
Accepted manuscript online:
(Fermi surface: calculations and measurements; effective mass, g factor)
Cite this article:
S. Şakiroĝlu, ü. Doĝan, A. Yldz, K. Akgüngör, H. Epik, Y. Ergün, H. Sari, and ì. Sökmen Ground state energy of excitons in quantum dot treated variationally via Hylleraas-like wavefunction 2009 Chin. Phys. B 18 1578
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