标题： 关于刘易斯-赖森费尔德（多多诺夫-马尔科）不变量方法 显示英文标题

标题： On the Lewis-Riesenfeld (Dodonov-Man'ko) invariant method

摘要： 我们根据先前引入的量子Arnold变换及其近期推广到量子Arnold-Ermakov-Pinney变换的情形，修正了求解量子时变谐振子的Lewis-Riesenfeld不变量方法。我们证明这两种方法是等价的，并展示了量子Arnold-Ermakov-Pinney变换相较于Lewis-Riesenfeld不变量方法的优势。我们表明，在量子时变阻尼谐振子中，Dodonov与Man'ko提出的不变量更为合适，并通过一些例子加以说明，重点关注阻尼情形。 显示英文摘要

摘要： We revise the Lewis-Riesenfeld invariant method for solving the quantum time-dependent harmonic oscillator in light of the Quantum Arnold Transformation previously introduced and its recent generalization to the Quantum Arnold-Ermakov-Pinney Transformation. We prove that both methods are equivalent and show the advantages of the Quantum Arnold-Ermakov-Pinney transformation over the Lewis-Riesenfeld invariant method. We show that, in the quantum time-dependent and damped harmonic oscillator, the invariant proposed by Dodonov & Man'ko is more suitable and provide some examples to illustrate it, focusing on the damped case.