论文标题
量子驱动系统的精确浮子解决方案
Exact Floquet solutions of quantum driven systems
论文作者
论文摘要
如何准确求解时间依赖性的schrödinger方程是一个有趣而重要的问题。在这里，我们提出了一种新的方法，以通过使用Floquet Theorem和时间依赖于时间依赖的单一转换来获得定期驱动系统的Schrödinger方程的精确Floquet溶液。使用该方法，我们为三个有趣的物理模型（线性电势模型，谐波振荡器模型和耦合的谐波振荡器模型）提供了波函数的精确浮部溶液。除了否定器外，我们还为谐波振荡器模型提供了浆果相的分析表达。此外，本文中提出的想法可以在数学中用于求解部分微分方程。
How to accurately solve time-dependent Schrödinger equation is an interesting and important problem. Here, we propose a novel method to obtain the exact Floquet solutions of the Schrödinger equation for periodically driven systems by using Floquet theorem and a time-dependent unitary transformation. Using the method, we give out the exact Floquet solutions of wave function for three interesting physical models -- linear potential model, harmonic oscillator model, and the coupled harmonic oscillator model in the presence of a periodic driving. In addition to the quasienergy, we also give out the analytic expression of Berry phase for the harmonic oscillator model. Moreover, the idea presented in this paper can be used in mathematics to solve partial differential equations.
