I cannot find anywhere on the web or on some books the esplicit expression for the time evolution of squeezed states (defined as $|\xi\rangle = S(\xi)|0\rangle = e^{\frac{1}{2}(\xi^*a^2-\xi (a^\dagger)^2)}|0\rangle$, where $|0\rangle$ is the harmonic oscillator ground state). I know they should be gaussian wave packet whose shape should evolve over time, but what's the esplicit expression for $|\xi(t)\rangle$? and for squeezed coherent states $|\xi,\alpha\rangle = D(\alpha)S(\xi)|0\rangle$? Moreover what is also the time-dependent expression for $\Delta x$ and $\Delta p$? They should oscillate over time, so that their product remains always equal to $\frac{\hbar}{2}$, but how?

Thank you in advance!


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