Abstract
We investigated the Gaussian Klauder coherent states for general time-dependent harmonic oscillator. We confirmed that the uncertainty product of general time-dependent harmonic oscillator in Gaussian Klauder coherent state is same as the minimum uncertainty product in number state. This is exactly agree with the theory for the standard harmonic oscillator developed by Fox et al. We applied our study to a damped harmonic oscillator and a harmonic oscillator with time-variable frequency that can be applied to a motion of an ion in a Paul trap. The uncertainty product in Gaussian Klauder coherent state fluctuated more or less as time goes by.
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