In their famous book [Quantum mechanics: non-relativistic theory. Course of Theoretical Physics, Vol. 3, Translated from the Russian by J. B. Sykes and J. S. Bell, Pergamon Press Ltd., London, 1958; MR0093319 (19,1230k)], L. D. Landau and E. M. Lifshits explained a result of Landau on the motion of a charged quantum particle (an electron) in a homogeneous magnetic field (the z-axis being taken in the direction of the field), and claimed that the charged quantum particle (electron) makes clockwise rotation on the xy-plane. They however applied a gauge transformation to the vector potential to perform explicit computation, and as a result their arguments in justifying their claim became not transparent. Adopting the vector potential without the gauge transformation and applying my theory, I give a transparent proof for the claim of Landau-Lifshits, namely, the quantum particle moves on the xy-plane as a two-dimensional quantum harmonic oscillator with an additional drift of clockwise rotation. I remark moreover another important point that this clockwise rotation will continue after the magnetic field is switched off.