Annihilation operator coherent states

Annihilation operator coherent states are the eigenstates of the annihilation operator and are parameterized by a complex eigenvalue. 

The last term in Eq. (116) describes the particle s interaction with a thermostat. We introduce the eigenfunctions and eigenvalues of creation and annihilation operators (coherent states) according to Ref. [50] ... 

The expectation value of H in the coherent state (7.17) can be evaluated explicitly for any Hamiltonian. However, an even simpler construction of Hd (valid to leading order in N) can be done (Cooper and Levine, 1989) by introducing intensive boson operators (Gilmore, 1981). In view of its simplicity, we report here this construction. If one divides the individual creation and annihilation operators by the square root of the total number of bosons, the relevant commutation relations become... 

The coherent states of the photon field can be defined as the eigenvectors of the annihilation operator... 

The Baker-Hausdorf formula cannot be used to solve this problem because the commutator of the annihilation as and creation a operators is not a c number. A numerical procedure, leading to the coefficients b was proposed by Buzek et al. [16]. In order to solve this problem analytically [18], it is of advantage to express the conventional coherent state, a), in the Fock representation in a different manner... 

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