量子动边界广义含时谐振子之精确的指数-正弦型演化态

研究了被局限于区间[0,L(t)]中运动的动边界广义含时谐振子量子系统,其Hamiltonian为坐标与动量的非齐次含时二次型.求出了具有“指数-正弦型”演化态的充要条件以及相应的正交归一完备的精确演化态系列.此结果不但几乎包含了已有结果作为特例,还涵盖了相当广泛的范围.此外,澄清了个别作者关于对时间的微商的一个误解,指出对时-空坐标的微商均具有寻常的含义.关键词：动边界量子系统广义含时谐振子演化态精确解

RIGOROUS EVOLVING STATES OF EXP-SIN TYPE FOR THE GENERALIZED TIME-DEPENDENT QUANTUM OSCILLATOR WITH A MOVING BOUNDARY

In this paper the generalized time-dependent quantum oscillator with a moving boundary is studied. Its Hamiltonian is of the non-homogeneous quadratic form of space-coordinate and momentum with time-dependent coefficients. We obtain an orthonormalized and complete set of rigorous evolving states of Exp-Sin type, as well as the necessary and sufficient condition for the existence of states of this type. Our results are of considerable generality, including as particular cases almost all the results given in literature. In addition, a misunderstanding of a few authors on the differential with respect to time is clarified and we point out that the differentiation with respect to either time or space-coordinate can be performed in the ordinary sense.