对数周期振子的波函数
Wavefunctios of log-periodic oscillators
摘要：
我们使用Lewis和Riesenfeld不变量方法[ \textit{J. Math. Phys.} \textbf{10}，1458（1969）]和幺正变换来获得具有对数周期型行为的含时谐振子的精确薛定谔波函数。对于每个振子，我们计算坐标和动量的量子涨落以及坐标和动量之间的量子关联。我们观察到具有$m=m_0t/t_0$和$ω= ω_0t_0/t$的谐振子表现出精确的对数周期振荡，其行为类似于具有$m$和$ω$常数的谐振子.
英文摘要：
We use the Lewis and Riesenfeld invariant method [\textit{J. Math. Phys.} \textbf{10}, 1458 (1969)] and a unitary transformation to obtain the exact Schrödinger wave functions for time-dependent harmonic oscillators exhibiting log-periodic-type behavior. For each oscillator we calculate the quantum fluctuations in the coordinate and momentum as well as the quantum correlations between the coordinate and momentum. We observe that the oscillator with $m=m_0t/t_0$ and $ω= ω_0t_0/t$, which exhibits an exact log-periodic oscillation, behaves as the harmonic oscillator with $m$ and $ω$ constant.
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