arXiv subjects
Publications and source records attributed to Yakov A. Korennoy.
Explicit expressions for most interesting quantum operators in optical tomography representation are found. General formalism of symbols of operators is presented in optical tomographic representation. The symbols of the operators are found explicitly for physical quantities.
Given a density operator $\hat ρ$ the optical tomography map defines a one-parameter set of probability distributions $w_{\hat ρ}(X,ϕ),\ ϕ\in [0,2π),$ on the real line allowing to reconstruct $\hat ρ$. We introduce a dual map from the special class $\mathcal A$ of quantum observables $\hat a$ to a special class of generalized functions $a(X,ϕ)$ such that the mean value $<\hat a>_{\hat ρ} =Tr(\hat ρ\hat a)$ is given by the formula $<\hat a>_{\hat ρ}= \int \limits_{0}^{2π}\int \limits_{-\infty}^{+\infty}w_{\hat ρ}(X,ϕ)a(X,ϕ)dXdϕ$. The class $\mathcal A$ includes all the symmetrized polynomials of canonical variables $\hat q$ and $\hat p$.
The evolution equation for the propagator of the quantum system in the optical probability representation (optical propagator) is obtained. The relations between the optical and quantum propagators for the Schrödinger equation and the optical propagator of an arbitrary quadratic system are found explicitly.