In this paper, the behavior of a heavy hole gas in a strongly prolate ellipsoidal Ge/Si quantum dot has been investigated. Due to the specific geometry of the quantum dot, the interaction between holes is considered one-dimensional. Based on the adiabatic approximation, it is shown that in the z-direction, hole gas is localized in a one-dimensional parabolic well. By modeling the potential of pair interaction between holes in the framework of oscillatory law, the problem is reduced to a one-dimensional, analytically solvable Moshinsky model. The exact energy spectrum of the few-hole gas has been calculated. A detailed analysis of the energy spectrum is presented. The character of long-wave transitions between the center-of-mass levels of the system has been obtained when Kohn theorem is realized.
Keywords: Kohn theorem; Moshinsky model; adiabatic approximation; ellipsoidal quantum dot; hole gas.