论文标题
在时间依赖的非交通空间中，阻尼的谐波振荡器的精确溶液
Exact solutions of a damped harmonic oscillator in a time dependent noncommutative space
论文作者
论文摘要
在本文中，我们获得了二维阻尼谐波振荡器的确切本征状状态。已经观察到，对于阻尼因子的某些特定选择和振荡器的时间依赖频率，从Ermakov-Pinney方程的解决方案中，存在依赖时间的非交通参数的有趣解决方案。此外，这些解决方案使我们能够获得将汉密尔顿特征状态与刘易斯不变的特征状态相关的阶段的精确分析形式。然后，我们获得了提高到有限任意功率的坐标运算符的矩阵元素的表达式。从这些一般结果中，我们计算了哈密顿量的期望值。对于与阻尼因子不同选择的Ermakov-Pinney方程的不同解和振荡器的时间依赖频率相对应的不同溶液，能量的期望值随时间而变化。
In this paper we have obtained the exact eigenstates of a two dimensional damped harmonic oscillator in time dependent noncommutative space. It has been observed that for some specific choices of the damping factor and the time dependent frequency of the oscillator, there exists interesting solutions of the time dependent noncommutative parameters following from the solutions of the Ermakov-Pinney equation. Further, these solutions enable us to get exact analytic forms for the phase which relates the eigenstates of the Hamiltonian with the eigenstates of the Lewis invariant. We then obtain expressions for the matrix elements of the coordinate operators raised to a finite arbitrary power. From these general results we then compute the expectation value of the Hamiltonian. The expectation values of the energy are found to vary with time for different solutions of the Ermakov-Pinney equation corresponding to different choices of the damping factor and the time dependent frequency of the oscillator.
