Functional Forms for the Squeeze and the Time-Displacement Operators

Abstract

Using Baker-Campbell-Hausdorff relations, the squeeze and harmonic-oscillator time-displacement operators are given in the form $\exp[δI] \exp[α(x^2)]\exp[β(x\partial)] \exp[γ(\partial)^2]$, where $α$, $β$, $γ$, and $δ$ are explicitly determined. Applications are discussed.