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

J Chem Phys. 2008 Feb 7;128(5):054101. doi: 10.1063/1.2827480.

Abstract

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.