Abstract
We introduce the dual vector | z,f (n)* of a single-mode nonlinear coherent state (NCS) by using the contour integral form of δ-function, and the explicit form of | z,f (n)* is obtained in enlarged Hilbert space. The nonlinear Fock states and their contour representation are deduced. A new completeness relation composed of | z,f (n)* and NCS in contour integral form is derived and its application in constructing a complex P-representation of density operators is shown.
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