广义非简谐振子的多尺度微扰理论(英文)

Multiple-Scale Perturbation Theory of Generalized Anharmonic Oscillator

应用多尺度微扰理论到广义非简谐振子,得到了一阶经典和量子微扰解．特别是我们的量子解在极限条件下能方便地转变为经典解,并且坐标和动量算符的对易关系的简化十分自然．与Taylor级数解相比较,无论是在经典还是在量子解中频率移动都出现在各阶振动表达式中,所以多尺度微扰解是弱耦合非简谐振动的较好解法．

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 an_harmonic oscillation than the Taylor series approach.