Ground state energy of excitons in quantum dot treated variationally via Hylleraas-like wavefunction

Abstract

In 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 rehk exp(−λreh) 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.