Uncertainty relations in quantum optics. Is the photon intelligent?

The Robertson–Schrödinger, Heisenberg–Robertson and Trifonov uncertainty relations for arbitrary two functions f1f1 and f2f2 depending on the quantum phase and the number of photons respectively, are given. Intelligent states and states which minimize locally the product of uncertainties (Δf1)2⋅(Δf2)2(Δf1)2⋅(Δf2)2 or the sum (Δf1)2+(Δf2)2(Δf1)2+(Δf2)2 are investigated for the cases f1=ϕ,exp(iϕ),exp(−iϕ),cosϕ,sinϕf1=ϕ,exp(iϕ),exp(−iϕ),cosϕ,sinϕ and f2=nf2=n.