Beam optics applications: quantum like versus classical-like domains

A review of the charged-particle beam optics in terms of recently developed approaches within both classical-like and quantum-like frameworks is presented. On the basis of the mutual connection of optics and mechanics, a brief overview of the quantum-like approach to electron optics is presented. In particular, the main results of the optical applications of the thermal wave model in phase space are given within the Wigner-Weyl picture. Furthermore, the tomographic approach in both classical-like and quantum-like domains in terms of the marginal-probability distribution is also presented. In particular, possible applications of the tomographic approach to optical problems with aberrations for accelerators are put forward. Some aspects of using quantum-like systems in quantum computing projects are discussed. (authors)