The linear partial differential equations(PDEs) of a lossy transmission line are first set up. We then fix the temporal frequency of operation and derive using spatial Fourier series representation of the voltage and current, a sequence of decoupled damped oscillator equations, which are then quantized using Lindblad/GKSL operators modeling the losses added to the lossless Harmonic Hamiltonian. The GKSL equations in Heisenberg form are shown to yield the correct damped quantum oscillator equations by making use of the canonical commutation relations for the creation and annihilation operators of the oscillators. We explain a scheme based on the Glauber-Sudarshan coherent state representation of how to transform the GKSL equation into partial differential equations for functions of time and complex variables. Quantum entropy computations are also made and finally MATLAB simulation of the GKSL is made which yield exponentially decaying graphs of a damped harmonic oscillator for the norms of observables evolving with time.

首先建立有损传输线的线性偏微分方程（PDE）。然后，我们固定操作的时间频率，并使用电压和电流的空间傅立叶级数表示导出一系列解耦阻尼振荡器方程，然后使用 Lindblad/GKSL 算子对添加到无损谐波哈密顿量的损耗进行建模。海森堡形式的 GKSL 方程显示为通过使用振荡器的创建和湮灭算符的规范对易关系来产生正确的阻尼量子振荡器方程。我们解释了一种基于 Glauber-Sudarshan 相干状态表示的方案，该方案如何将 GKSL 方程转换为时间和复变量函数的偏微分方程。