Coherent states Fock representation

Within the theoretical framework of time-dependent Hartree-Fock theory, Suzuki has proposed an initial-value representation for a spin-coherent state propagator [286]. When we adopt a two-level system with quantum Hamiltonian H, this propagator reads... 

Now, returning to Pfeifer s model of chirality we see that we have to make a choice of representation when selecting states to use in a Hartree variational calculation of the ground-state of the molecule-radiation field system. In Pfeifer s calculations the trial functions are chosen as coherent states, say t/N based on the photon Fock space n) in the Coulomb gauge theory an inequivalent set of trial functions is obtained by choosing coherent states, ip, based on the gauge-invariant photon Fock space n). One then has to compare the results of two minimization calculations involving, (cf. Eq. 5.4),... 

This work is intended as an attempt to present two essentially different constructions of harmonic oscillator states in a FD Hilbert space. We propose some new definitions of the states and find their explicit forms in the Fock representation. For the convenience of the reader, we also bring together several known FD quantum-optical states, thus making our exposition more self-contained. We shall discuss FD coherent states, FD phase coherent states, FD displaced number states, FD Schrodinger cats, and FD squeezed vacuum. We shall show some intriguing properties of the states with the help of the discrete Wigner function. 

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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