论文标题
通过Lewis-Riesenfeld动力不变方法，具有时间相关的量子谐波振荡器的精确解决方案
Exact solution of a time-dependent quantum harmonic oscillator with two frequency jumps via the Lewis-Riesenfeld dynamical invariant method
论文作者
论文摘要
在过去的几十年中，几位作者对其频率有多次突然跳跃的谐波振荡器进行了研究。我们调查了具有初始频率$ω_0$的量子谐波振荡器的动力学，该动力会突然跳至频率$ω_1$，并且在一定时间间隔后突然返回其初始频率。考虑到初始状态不同于基本状态，使用了平均能量值，平均激发数和过渡概率的表达式，使用刘易斯 - 里森菲尔德方法的刘易斯 - 里森菲尔德方法。我们表明，即使在$ω_1<ω_0$时，振荡器的平均能量在跳跃后的平均能量等于或大于跳跃之前的平均能量。我们还表明，对于跳跃之间的时间间隔的特定值，振荡器返回到同一初始状态。
Harmonic oscillators with multiple abrupt jumps in their frequencies have been investigated by several authors during the last decades. We investigate the dynamics of a quantum harmonic oscillator with initial frequency $ω_0$, that undergoes a sudden jump to a frequency $ω_1$ and, after a certain time interval, suddenly returns to its initial frequency. Using the Lewis-Riesenfeld method of dynamical invariants, we present expressions for the mean energy value, the mean number of excitations, and the transition probabilities, considering the initial state different from the fundamental. We show that the mean energy of the oscillator, after the jumps, is equal or greater than the one before the jumps, even when $ω_1<ω_0$. We also show that, for particular values of the time interval between the jumps, the oscillator returns to the same initial state.
