Squeezed States of the Generalized Minimum Uncertainty State for the Caldirola-Kanai Hamiltonian

Details Squeezed States of the Generalized Minimum Uncertainty State for the Caldirola-Kanai Hamiltonian Squeezed States of the Generalized Minimum Uncertainty State for the Caldirola-Kanai Hamiltonian

2003-08-30

arxiv.org/abs/quant-ph/0309003v1

J. Phys. A: Math. Gen. 36 (2003) 12089-12095

Physics

Quantum Physics

RevTex4, 9 pages, no fingure; to be published in Journal of Physics A

Scientific paper

10.1088/0305-4470/36/48/011

We show that the ground state of the well-known pseudo-stationary states for the Caldirola-Kanai Hamiltonian is a generalized minimum uncertainty state, which has the minimum allowed uncertainty $\Delta q \Delta p = \hbar \sigma_0/2$, where $\sigma_0 (\geq 1)$ is a constant depending on the damping factor and natural frequency. The most general symmetric Gaussian states are obtained as the one-parameter squeezed states of the pseudo-stationary ground state. It is further shown that the coherent states of the pseudo-stationary ground state constitute another class of the generalized minimum uncertainty states.

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