用算符分解方法计算非同调谐振子几何相位及其推广

Calculation and Generalization of Non-Adiabatic Geometric Phase of Isotonic Oscillator with Operator Decomposition

将几何相位理论应用于非同调谐振子(isotonicoscillator缩写为IO)这类量子系统,运用算符分解方法计算了系统在二态体系的AharonovAnandan相位,推广至三态及多态体系,并讨论了AA相位更普遍的计算公式和变化规律.

Operator decomposition approach is used to calculate the non-adiabatic geometric phase of anharmonic oscillator. As an example we focus on the isotonic oscillator, a type of anharmonic oscillator. The Aharonov-Anandan phase is derived when we choose the ground state and the first excited state as cyclic initial states. Then we generalize our result by choosing three states or more states as cyclic initial states. Finally, we give a general formula of Aharonov-Anandan phase for time-independent systems and discuss its applicability.