Functional Forms for the Squeeze and the Time-Displacement Operators

Using Baker-Campbell-Hausdorff relations, the squeeze and harmonic-oscillator time-displacement operators are given in the form $\exp[\delta I] \exp[\alpha (x^2)]\exp[\beta(x\partial)] \exp[\gamma (\partial)^2]$, where $\alpha$, $\beta$, $\gamma$, and $\delta$ are explicitly determined. Applications are discussed.