论文标题
一般动力不变的一般性及其统一关系的时间依赖于三个耦合量子振荡器
Formulation of general dynamical invariants and their unitary relations for time-dependent three coupled quantum oscillators
论文作者
论文摘要
得出了三个耦合时间依赖性振荡器的一般动力不变操作员。尽管获得的不变式操作员满足了liouville-von neumann方程，但由于参数的时间变化的任意性，其数学公式在某种程度上变得有些复杂。肯定指定了制定此不变的参数条件。通过使用统一转换方法，不变的操作员被转换为与三个独立的简单谐波振荡器相对应的操作员。与如此简化的不变性相关的众所周知的量子解决方案的反变换使我们能够识别耦合原始系统的量子解决方案。这些解决方案是准确的，因为我们不仅不仅使用近似值来制定不变的操作员，而且不使用统一转换。此处提供的不变运算符及其本征函数可用于表征系统的量子特性，这些量子特性具有各种与时间相关的参数类型的选择。
A general dynamical invariant operator for three coupled time-dependent oscillators is derived. Although the obtained invariant operator satisfies the Liouville-von Neumann equation, its mathematical formula is somewhat complicated due to arbitrariness of time variations of parameters. The parametric conditions required for formulating this invariant are definitely specified. By using the unitary transformation method, the invariant operator is transformed to the one that corresponds to three independent simple harmonic oscillators. Inverse transformation of the well-known quantum solutions associated with such a simplified invariant enables us to identify quantum solutions of the coupled original systems. These solutions are exact since we do not use approximations not only in formulating the invariant operator but in the unitary transformation as well. The invariant operator and its eigenfunctions provided here can be used to characterize quantum properties of the systems with various choices of the types of time-dependent parameters.
