On Cyclic Harmonic Oscillators

Abstract

It is proven that the energy of a quantum mechanical harmonic oscillator with a generically time-dependent but cyclic frequency, ${\omega }_0(t_0)={\omega }_0(0)$, cannot decrease on the average if the system is originally in a stationary state, after the system goes through a full cycle. The energy exchange always takes place in the direction from the macroscopic system (environment) to the quantum microscopic system.

Latex file, 14 pages, 3 figures, minor correction made in Section 1