论文标题
谐波振荡器及其表示的时间操作员
Time Operators of Harmonic Oscillators and Their Representations
论文作者
论文摘要
一维谐波振荡器的时间操作员$ \ hat t_ \ eps $ $ \ hat h_ \ eps = \ half（p^2+\ eps q^2）$是严格构造的。它正式表示为$ \ hat t_ \ eps = \ frac {1} {\ sqrt \ eps}（\ arctan（\ arctan）（\ sqrt \ eps \ eps \ hat t_0）+\ arctan+arctan（\ sqrt \ sqrt \ sqrt \ eps \ hat t_1） t_1 = qp^{ - 1} $。结果表明，从sesqui-linear形式的意义上讲，规范的换向关系$ [h_ \ eps，\ hat t_ \ eps] = - i \一个$在密集的域上呈现，并且显示了$ \ hat t_ \ eps $的极限为$ \ eps \ eps \ eps \ 0 $。最后给出了$ \ hat t_ \ eps $的矩阵表示及其分析延续。
A time operator $\hat T_\eps$ of the one-dimensional harmonic oscillator $ \hat h_\eps=\half(p^2+\eps q^2)$ is rigorously constructed. It is formally expressed as $ \hat T_\eps=\half\frac{1}{\sqrt \eps } (\arctan (\sqrt \eps \hat t_0)+\arctan (\sqrt \eps \hat t_1))$ with $\hat t_0=p^{-1}q$ and $\hat t_1=qp^{-1}$. It is shown that the canonical commutation relation $[h_\eps, \hat T_\eps ]=-i\one$ holds true on a dense domain in the sense of sesqui-linear forms, and the limit of $\hat T_\eps $ as $\eps\to 0$ is shown. Finally a matrix representation of $\hat T_\eps$ and its analytic continuation are given.
