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Quasi-coherent states for the Hermite oscillator. (English) Zbl 1391.81096
Summary: In this study, we obtained the quasi-coherent states of the damped harmonic oscillator which satisfy the Hermite differential equation classically. For the general damped oscillator, the Gaussian wave packets were derived in configuration and momentum spaces with minimum uncertainities at $$t = 0$$, and the quasi-stationary states also obtained and showed that the expansion coefficients give a time-dependent Poisson distribution. As a special case, we found the displaced Gaussian wave packets for the Hermite oscillator and also discussed the weak coupling limit of the wave packets.