含时量子系统传播子的ABCD形式

ABCD formulation of propagator of a time dependent quantum system

将含时量子系统状态的演化看成物质波波束沿时间轴的传输 ,引入束宽、发散角、曲率半径、品质因子和束熵表征波束的传输 .发现品质因子守恒的量子系统 ,其动量算子和位置算子呈线性演化 ,传播子可以表达成ABCD的形式 ,最小波包 (品质因子为 1 )的形式不随时间改变 .

The evolution of states of a time dependent quantum system can be supposed to be the propagation of a matter wave beam along the time coordinate. The beam width, divergence, curvature radius, quality factor and entropy were introduced to represent the matter wave beam. For a quantum system with a conservative beam quality factor, the evolutions of position operator and momentum operator are linear, the propagator is of the ABCD formulation, and the formulation of the minimum wave packet, of which the quality factor is unity, is time independent. The applications of these to quantum systems of constant potential and oscillators were also discussed.