Abstract
In this paper, the behavior of the few-body electron gas localized in a strongly prolate ellipsoidal quantum dot with the presence of the uniform external magnetic field has been investigated. Due to the specific geometry of the quantum dot it has been shown that the motion of the particles in the considered system can be separated into fast and slow, in the XOY plane and along the OZ direction respectively. Based on the adiabatic approach it has been shown that in the direction of the slow motion the electron gas is localized in the one-dimensional parabolic quantum well. If a long-wavelength radiation falls on the system, then due to the parabolic form of the confining potential, conditions occur to implement the generalized Kohn theorem for this system.
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