Quantum and Quasi-classical States of the Photon Phase Operator

Quantization in Polar Coordinates and the Phase Operator

“…Then the operator domains contain ^(R), which is defined by N, and is the natural arena for the unbounded operators of quantum mechanics [4,5]. A number of authors have considered the operator of multiplication by the angle on the Hilbert space L 2 (T) over the circle [6,7], or certain subspaces of it [8]. The resulting operator, which we shall denote A (3), can then be transported to the Schrodinger representation, which we shall do in the third section.…”

Regular phase operator and SU(1,1) coherent states of the harmonic oscillator

“…We note that the possibility of using a finite-dimensional space in this context has already been discussed by Jordan (1927). The differences of the Garrison-Wong (1970) and Pegg-Barnett (1989) formalism have been thoroughly investigated by Popov and Yarunin (1992) and Gantsog et al (1992). The limit matrix elements of the phase operator in number representation (as we let the dimension of the Hilbert space going to infinity) obtained by these authors have already been presented by Weyl (1931).…”

“…the book by Cooke (1950), which has also been quoted by Popov and Yarunin (1992) in this context). Accordingly, the two infinite series on the right hand side of (2.10)…”

“…This is also the source of that difficulty that the powers of GW  , expressed in the Fock basis, are very complicated (see Popov and Yarunin, 1992). In this context we note that Gantsog, Miranowicz and Tanaś (1992) have performed a thorough analysis of the phase distributions based on the eigenstates of GW  , and made a comparison with the predictions based on the formalism introduced by Pegg and Barnett (1989).…”

“…The limit of the symmetric double sum in (2.13) still exists, and represents the phase operator GW  of Garrison and Wong (1970), as has been emphasized by Popov and Yarunin (1992).…”