  The electron motion in rather strong magnetic fields (when only the lowest
Landau level is populated) is considered. In this case the electron kinetic
energy is frozen out and the electrons are guided by slowly varied potential.
Using the adiabatic procedure and expansion in magnetic length series the
approximate description is developed. In zero order this approximation leads to
the classical equations of motion describing the Larmor circle drift in the
potential gradient. In the second order the special quantum mechanical
description where the electron potential energy plays the role of the total
Hamiltonian is constructed. Simple examples of a single and two electrons in
the parabolic dot demonstrates that the proposed approximate description gives
the main features of the electron system spectrum and the collective phenomena.
