Coherent states of general time-dependent harmonic oscillator |
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Authors: | Jeong Ryeol Choi |
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Institution: | (1) Department of New Material Science, Division of Natural Sciences, Sunmoon University, 336-708 Asan, Republic of Korea |
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Abstract: | By introducing an invariant operator, we obtain exact wave functions for a general time-dependent quadratic harmonic oscillator.
The coherent states, both inx- andp-spaces, are calculated. We confirm that the uncertainty product in coherent state is always larger thankh/2 and is equal to the minimum of the uncertainty product of the number states. The displaced wave packet for Caldirola-Kanai
oscillator in coherent state oscillates back and forth with time about the center as for a classical oscillator. The amplitude
of oscillation with no driving force decreases due to the dissipation in the system. However, the oscillation with resonant
frequency oscillates with a large amplitude, even after a sufficient time elapse. |
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Keywords: | Time-dependent harmonic oscillator invariant operator coherent state |
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