The q-analog coherent states \ensuremath{\Vert}z
〉q are used to identify some of the canonical physical properties of the single-mode q-analog quantized radiation field in the \ensuremath{\Vert}z
〉q ``classical limit'' where \ensuremath{\Vert}z\ensuremath{\Vert} is large. In this quantum-optics-like limit, the fractional uncertainties of most physical quantities (momentum, position, amplitude, phase) which characterize the quantum field are shown to be O(1), and only vanish as O(1/\ensuremath{\Vert}z\ensuremath{\Vert}) when q=1. In contrast to this more-quantum-like behavior for q\ensuremath{\ne}1, the fractional uncertainties do still approach zero for the usual number operator, N, and the N-Hamiltonian
HN\ensuremath{\equiv}\ensuremath{\Elzxh}\ensuremath{\omega}(N+1/2) which describes a free q-boson gas. An empirical signature for q-boson counting statistics is that (\ensuremath{\Delta}N
)2/〈N〉\ensuremath{\rightarrow}0 as \ensuremath{\Vert}z\ensuremath{\Vert}\ensuremath{\rightarrow}\ensuremath{\infty}. Properties of the q-analog generalizations of the phase operators of Susskind and Glogower (SG) and of the phase operator \ensuremath{\varphi}${\mathrm{^}}_{\mathit{q}}$ of Pegg and Barnett are investigated. In contrast to the manifest q deformed properties of SG operators for moderate \ensuremath{\Vert}z${\mathrm{\ensuremath{\Vert}}}^{2}$, the ``Hermitian'' phase operator \ensuremath{\varphi}${\mathrm{^}}_{\mathit{q}}$ still exhibits almost normal classical behavior in the \ensuremath{\Vert}z
〉q basis. In particular, the conventional (approximate) number-phase uncertainty relation \ensuremath{\Delta}N\ensuremath{\Delta}\ensuremath{\varphi}${\mathrm{^}}_{\mathit{q}}$\ensuremath{\ge}1/2 and approximate commutation relation [N,\ensuremath{\varphi}${\mathrm{^}}_{\mathit{q}}$]=i are found to follow for the single-mode q-analog quantized field. So N and \ensuremath{\varphi}${\mathrm{^}}_{\mathit{q}}$ are almost canonically conjugate operators in the \ensuremath{\Vert}z
〉q classical limit. The \ensuremath{\Vert}z
〉q coherent states minimize this uncertainty relation for moderate \ensuremath{\Vert}z${\mathrm{\ensuremath{\Vert}}}^{2}$. q-analog generalizations of the P, Q, and W phase-space representations are treated in the Appendix.
The q-analogue coherent states {vert_bar}z >{sub q} are used to identify physical signatures for the presence of a q-analogue quantized radiation field in the {vert_bar} >{sub q} classical limit where {vert_bar}z{vert_bar} is large. In this quantum-optics-like limit, the fractional uncertainties of most physical quantities (momentum, position, amplitude, phase) which characterize the quantum field are O(1). They only vanish as O(1/{vert_bar}z{vert_bar}) when q = 1. However, for the number operator, N, and the N-Hamiltonian for a free q-boson gas, H{sub N} = {Dirac_h}{omega}(N + 1/2), the fractional uncertainties do still approach zero. A signature for q-boson counting statistics is that ({Delta}N){sup 2}/<N> {yields} 0 as {vert_bar}z{vert_bar} {yields} {infinity}. Except for its O(1) fractional uncertainty, the q-generalization of the Hermitian phase operator of Pegg and Barnett, {phi}{sub q}, still exhibits normal classical behavior. The standard number-phase uncertainty-relation, {Delta}N {Delta}{phi}{sub q} = 1/2, and the approximate commutation relation, [N,{phi}{sub q}] = i, still hold for the single-mode q-analogue quantized field. So, N and {phi}{sub q} are almost canonically conjugate operators in the {vert_bar}z >{sub q} classical limit. The {vert_bar}z >{sub q} CS`s minimize this uncertainty relation for moderate {vert_bar}z{vert_bar}{sup 2}.
We have studied the statistical and squeezing properties of the cavity light generated by a two-level laser. This optical system contains N two-level atoms available in a cavity coupled to a single-mode vacuum reservoir. They are pumped to the top level from the bottom level by means of the electron bombardment. Applying the steady-state solutions of the equations of evolution of the expectation values of the atomic operators and the quantum Langevin equation, we obtained the global and local photon statistics of the single-mode light beam. We have found that, for the two-level laser operating well above the threshold, the uncertainties in the plus and minus quadratures are equal and satisfy the minimum uncertainty relation. In view of this, we have identified the light generated by the laser operating well above threshold to be coherent. On the other hand, the light generated by the laser operating at threshold is found to be chaotic. From the obtained results, we have also observed that a large part of the local mean photon number, the local photon number variance, and the local quadrature variance are confined in a relatively narrow frequency interval.