In this work, we analyze the quantum dynamics of a generalized pendulum with a time-varying mass increasing exponentially and constant gravitation. By using Lewis–Riesenfeld invariant approach and Fock states, we solve the time-dependent Schrödinger equation for this system and write its solutions in terms of solutions of the Milne–Pinney equation. We also construct coherent states for the quantized pendulum and use both Fock and coherent states to investigate some important physical proprieties of the quantized pendulum such as eigenvalues of the angular displacement and momentum, their quantum variances as well as the respective uncertainty principle. Finally, we derive the geometric, dynamical and Berry phases for the time-dependent generalized pendulum.

中文翻译：

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广义阻尼摆的量子运动、相干态和几何相位

在这项工作中，我们分析了质量随时间变化的质量呈指数增长且引力恒定的广义摆的量子动力学。通过使用 Lewis-Riesenfeld 不变量方法和 Fock 状态，我们求解了该系统的瞬态薛定谔方程，并根据 Milne-Pinney 方程的解写出它的解。我们还为量子化摆构造了相干态，并使用福克和相干态来研究量子化摆的一些重要物理性质，例如角位移和动量的特征值、它们的量子方差以及各自的不确定性原理。最后，我们推导出时间相关广义摆的几何、动力学和贝里相位。