Radiation phase states

The unit operator here coincides with (61). Thus, the states (72) form a basis in the Hilbert space (60) dual to the basis of conventional number states nm). In analogy to the atomic phase states (46), we call (72) the radiation phase states of the electric dipole photons. It follows from (69) that the radiation phase states (72) are the eigenstates of the operator ... 

In contrast to the relation (45), the eigenvalues of in (73) contain, in addition to the exponential, a factor of vm, describing the number of photons in a given radiation phase state. Thus, this is an non-normalized exponential of the phase operator. 

Although the canonical transformation (67) has the very simple form of the finite Fourier transformation, the connection between the conventional number states and the radiation phase states (72) is not simple ... 

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