A semiclassical study of forced anharmonic oscillators

In this paper we develop semiclassical equations of motion for the forced anharmonic oscillator. Both the main and the overtone resonances were explicitly considered. The general formalism was applied to the Duffing oscillator, whose periodic solutions for the main and the third overtone resonances were calculated. The classical and the semiclassical solutions are very similar, the only qualitative difference being the disappearance of the unstable classical solutions.