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Explicit state vector for Torres-Vega-Frederick phase space representation and its statistical behavior.

We find the explicit state vector for Torres-Vega-Frederick phase space representation [Go. Torres-Vega and J. H. Frederick, J. Chem. Phys. 98, 3103 (1993)], denoted by Gamma. This set of states make up a complete and nonorthogonal representation. The Weyl ordered form of Gamma Gamma [see text for the sign] is derived, which can clearly exhibit the statistical behavior of marginal distribution of Gamma Gamma [see text for the sign]. The minimum uncertainty relation for mid R:Gamma is demonstrated, which shows it being a coherent squeezed state.