Abstract
Generalized coherent states which are associated with the multiplicative group of non-zero complex numbers are introduced. They have the property of temporal stability, and they form a total set in some subspace of the full Hilbert space. They are highly non-classical states, in the sense that in general, their Bargmann functions have zeros which are related to regions where their Wigner functions take negative values. States with Bargmann functions sin (πAz) and exp (Bz)/[Γ(Az)]k are examples of the general formalism, and they are discussed in detail.
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