论文标题
点转换：量子依赖性质量非平稳振荡器的精确解
Point transformations: exact solutions of the quantum time-dependent mass nonstationary oscillator
论文作者
论文摘要
在本说明中，我们解决了由振荡器样相互作用与频率和质量项依赖于时间组成的时间相关的哈密顿量的精确解。后者是通过构造适当的点变换来实现的，以使其将固定振荡器的schrödinger方程变形为时间依赖性模型之一。因此，后者的溶液可以看作是固定振荡器众所周知的溶液的变形，因此可以直接确定一组正交溶液。后者是可能的，因为内部产品结构由点转换保留。同样，固定振荡器的任何不变算子都将变成时间依赖模型的不变式。该属性导致一种直接的方法来确定运动常数，而无需使用Ansatz。
In this note we address the exact solutions of a time-dependent Hamiltonian composed by an oscillator-like interaction with both a frequency and a mass term that depend on time. The latter is achieved by constructing the appropriate point transformation such that it deforms the Schrödinger equation of a stationary oscillator into the one of the time-dependent model. Thus, the solutions of the latter can be seen as deformations of the well known solutions of the stationary oscillator, and thus an orthogonal set of solutions can be determined in a straightforward way. The latter is possible since the inner product structure is preserved by the point transformation. Also, any invariant operator of the stationary oscillator is transformed into an invariant of the time-dependent model. This property leads to a straightforward way to determine constants of motion without requiring to use ansatz.
