In a number of previous papers authors have introduced quasiparticle of radio- and optical systems. We have called this quasiparticle by ‘radion’. The basis for this is the representation of Green’s function of equation of quasioptics by Feynman integral. It means that radion has quantum mechanical properties. In particular in approximation of quasioptics one can interprete amplitude of electromagnetic field as amplitude of probability of radion. In the paper presented we describe new features of radion which we have established recently namely we have found some exact solutions of evolutionary equation for field of quantum mechanical averages of momenta of ensemble of radions possessing by average of momentum in initial state depending on average of coordinate in it. We demonstrate three the simplest solutions from this set of exact solutions. These solutions in the form of power series on dimensionless time are applicable up to the moment of gradient catastrophe. For representation of solutions of parabolic equation in approximation of quasioptics Remizov method of quasi-Feynman formulae has been used. All these results due to suggested by us physical analogy are valid for free one-dimensional nonrelativistic quantum mechanical particle too. Also in the framework of Remizov method a number of new formulae for statistical radiophysics and optics has been obtained. ‘Natural’ fractality of radio- and optical systems has been discussed.