Lai Meng-Yun, Pan Xiao-Yin
Department of Physics, Ningbo University, Ningbo, 315211, China.
Sci Rep. 2016 Oct 17;6:35412. doi: 10.1038/srep35412.
We investigate the evolution of the many-body wave function of a quantum system with time-varying effective mass, confined by a harmonic potential with time-varying frequency in the presence of a uniform time-varying magnetic field, and perturbed by a time-dependent uniform electric field. It is found that the wave function is comprised of a phase factor times the solution to the unperturbed time-dependent Schrödinger equation with the latter being translated by a time-dependent value that satisfies the classical driven equation of motion. In other words, we generalize the harmonic potential theorem to the case when the effective mass, harmonic potential, and the external uniform magnetic field with arbitrary orientation are all time-varying. The results reduce to various special cases obtained in the literature, particulary to that of the harmonic potential theorem wave function when the effective mass and frequency are both static and the external magnetic field is absent.
我们研究了一个量子系统的多体波函数的演化，该系统具有随时间变化的有效质量，被一个频率随时间变化的谐振势所束缚，处于均匀随时间变化的磁场中，并受到一个随时间变化的均匀电场的扰动。结果发现，波函数由一个相位因子乘以未受扰动的含时薛定谔方程的解组成，其中后者被一个满足经典驱动运动方程的随时间变化的值平移。换句话说，我们将谐振势定理推广到有效质量、谐振势以及任意取向的外部均匀磁场均随时间变化的情况。这些结果归结为文献中得到的各种特殊情况，特别是当有效质量和频率均为静态且不存在外部磁场时的谐振势定理波函数的情况。
