Multiple-Scale Perturbation Theory of Generalized Anharmonic Oscillator

Abstract：

Classical and quantum oscillator of generalized anharmonicity is solved analytically up to the linear power of ε by using the multiple-scale perturbation method. The commutation relation of position and momentum operator can be simplified easily and the quantum solutions transformed into the classical form conveniently under the extreme conditions, which are different from the earlier multiple-scale perturbation theory. Moreover compared with the Taylor series solution, the frequency shifts in our solutions appear in the expression of oscillations of all orders in both classical and quantum cases, so multiple-scale perturbation method is more suitable for solving the weak-coupling anharmonic oscillation than the Taylor series approach.