论文标题
在空间中对1D强制谐波振荡器的量化（$ x，v $）
Quantization of the 1-D forced harmonic oscillator in the space ($x, v$)
论文作者
论文摘要
使用量子变量（$ x，\ hat v $）研究强制谐波振荡器的量化，并使用换向关系$ [x，\ hat v] = i \ hbar/m $，并在这些变量上使用shrödinger的等式，并将线性操作员与量化的量化相关联，并将量子与量化$ k（x，x，x，v，v，v，t）进行比较。 （$ x，p $）使用hamiltonian $ h（x，p，t）$的通常的schrödinger方程来完成，并使用换向关系$ [x，\ hat p] = i \ hbar $。发现对于非谐音情况，两种量化形式都带来了相同的结果。但是，对于共鸣的情况，两种量化形式都是不同的，并且该系统处于（$ x，\ hat v $）量化的退出状态的可能性较小，而不是（$ x，\ hat p $）量化的（$ x，\ hat p $）量化，系统的平均能量在（$ x，\ hat p $）上的平均量化量和$ x，x，x，x，x，\ hat v $（x，x，\ shon）量更高。 （$ x，\ hat p $）量化高于（$ x，\ hat v $）量化。
The quantization of the forced harmonic oscillator is studied with the quantum variable ($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.
