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See coherent state and squeezed coherent state for more details.
The most general wave function that satisfies the identity above is the squeezed coherent state (we work in units with )
BCS wave function is an example of squeezed coherent state of fermions.
In physics, a squeezed coherent state is any state of the quantum mechanical Hilbert space such that the uncertainty principle is saturated.
Via certain nonlinear interactions, a coherent state can be transformed into a squeezed coherent state, which can exhibit super- or sub-Poissonian photon statistics.
Only in an exotic squeezed coherent state can the number of photons measured per unit time have fluctuations smaller than the square root of the expected number of photons counted in that period of time.