arXiv 2005.003442020-05quant-ph

空间（$x, v$）中一维受迫谐振子的量子化

Quantization of the 1-D forced harmonic oscillator in the space ($x, v$)

Gustavo Lopez, Omar Bravo

备注：: 3 figures, 11 pages

摘要：

用量子变量研究了受迫谐振子的量子化（$x,\hat v$），利用对易关系$[x,\hat v]=i\hbar/m$，对这些变量使用类薛定谔方程，并将线性算子与经典系统的运动常数$K(x,v,t)$联系起来，与空间量子化进行了比较（$x,p$）是用哈密顿量$H(x,p,t)$的常用薛定谔方程和对易关系$[x,\hat p]=i\hbar$来完成的。结果表明，在非共振情况下，两种量子化形式的结果是一致的。然而，对于共振情况，两种形式的量子化是不同的，并且系统处于激发态的概率为（$x,\hat v$）量化的振荡比（$x,\hat p$）量子化时，系统的平均能量较高，（$x,\hat p$）量化比在$(x,\hat v$）量化上，并且（$x,\hat p$）量化上的玻尔兹曼-香农熵高于（$x,\hat v$）量化上的玻尔兹曼-香农熵。

英文摘要：

The quantization of the forced harmonic oscillator is studied with the quantum variable ($x,\hat v$), with the commutation relation $[x,\hat v]=i\hbar/m$, and using a Shrödinger's like equation on these variable, and associating a linear operator to a constant of motion $K(x,v,t)$ of the classical system, The comparison with the quantization in the space ($x,p$) is done with the usual Schrödinger's equation for the Hamiltonian $H(x,p,t)$, and with the commutation relation $[x,\hat p]=i\hbar$. It is found that for the non resonant case, both forms of quantization brings about the same result. However, for the resonant case, both forms of quantization are different, and the probability for the system to be in the exited state for the ($x,\hat v$) quantization has less oscillations than the ($x,\hat p$) quantization, the average energy of the system is higher in ($x,\hat p$) quantization than on the $(x,\hat v$) quantization, and the Boltzmann-Shannon entropy on the ($x,\hat p$) quantization is higher than on the ($x,\hat v$) quantization.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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英文摘要：

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