We present a simple and direct phenomenological quantization scheme for the London superconductor. Using Maxwell and continuity equations, we show that this quantization can be mapped into a quantum damped harmonic oscillator which is described by the Caldirola-Kanai Hamiltonian. With the help of the dynamic invariant method, we solve the time-dependent Schrödinger equation associated with this Hamiltonian and write its solutions in terms of a particular solution of the Milne-Pinney equation. Based on the Fock states representation, we also demonstrate that our quantization model is similar to that of the standard mechanical harmonic oscillator. Finally, we evaluate some important physical quantities of this superconductor such as expectation values of the charge and magnetic flux and their variances and the respective uncertainty principle.

我们为伦敦超导体提出了一种简单直接的现象学量化方案。使用麦克斯韦方程和连续性方程，我们表明该量化可以映射到由Caldirola-Kanai Hamiltonian描述的量子阻尼谐波振荡器。借助动态不变方法，我们求解了与该哈密顿量相关的时变Schrödinger方程，并根据Milne-Pinney方程的特定解来写其解。基于Fock状态表示，我们还证明了我们的量化模型与标准机械谐波振荡器的相似。最后，我们评估了这种超导体的一些重要物理量，例如电荷和磁通量的期望值及其方差和各自的不确定性原理。