一维含时受迫量子谐振子系统的严格解和量子相位

Exact Solution and Geometric Phases for a One-dimensional Time-dependent Driven Quantum Harmonic Oscillator

运用广义线性量子变换普遍理论对一维含时受迫量子谐振子系统进行求解,给出了其演化算符和其唯一严格解,然后运用相位理论给出了系统的量子相位,重点探讨了其非绝热非循回几何相位、Aharonov-Anandan相位在循回条件与绝热近似条件下的普遍结果及相互之间的转化关系,并应用求解了一个具体的一维含时受迫谐振子这个特例研究表明Berry相是非绝热非循回几何相位与Aharonov-Anandan相的零级近似.

The unique exact solution of the evolution operator for a one-dimensional time-dependent driven quantum harmonic oscillator is obtained by means of generalized linear quantum transformation theory. The non-adiabatic non-cyclic geometric phase,Aharonov-Anandan phase,Berry phase,cyclic conditions and adiabatic approximation conditions are also investigated by the phase theory of quantum phase system. As a specific example,a time-dependent forced harmonic oscillator is addressed. It is shown that Berry phase is the zeroth-order approximation of the non-adiabatic non-cyclic geometric phase or Aharonov-Anandan phase of the system.