四次非简谐振子的多尺度微扰理论

应用多尺度微扰理论研究了弱耦合非简谐参数的经典和量子四次非谐振子,得到了四次非简谐运动方程的经典和量子二阶解.此解与以前同类问题的多尺度微扰解不同,在Heisenberg表象中坐标和动量算符的对易关系的简化十分自然,并且量子解能十分方便地过渡到经典解.

Multiple-Scale Perturbation Theory of Quartic Anharmonic Oscillator

Classical and quantum oscillators of quartic anharmonicity are solved analytically up to the second power of(weak-coupling constant) by using the multiple-scale perturbation theory.In Heisenberg picture the difference from the earlier multiple-scale perturbation solution is that the commutation relation of coordinate and momentum operator is naturally simplified and it is very convenient to get classical result from quantum one in limit condition.