In this work, we analyze the quantum dynamics of a particle with time-varying mass increasing exponentially in a Paul trap with a trap frequency that decays exponentially with time. By making use of the Lewis-Riesenfeld invariant theory and Fock states, we solve the time-dependent Schrödinger equation for this problem and employ its solutions to construct coherent states for the quantized particle in the Paul trap. We also use both Fock and coherent states to calculate some quantities of physical interest of this system such as expectation values of the position and momentum coordinates, their variances and the respective uncertainty principle.

中文翻译：

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Paul阱中阻尼粒子的量子运动

在这项工作中，我们分析了在Paul阱中具有随时间变化的质量随时间呈指数增长的质点的粒子的量子动力学。通过使用Lewis-Riesenfeld不变量理论和Fock状态，我们解决了该问题的时变Schrödinger方程，并利用其解为Paul陷阱中的量化粒子构造了相干态。我们还使用Fock和相干态来计算该系统的一些物理量，例如位置和动量坐标的期望值，它们的方差以及各自的不确定性原理。