The centrally-symmetric solutions of electronic excitations of semiconductors in the conditions of relativistic like degeneracy of dynamical properties

Abstract

The excited states of materials with the structure of crystals were analyzed in the paper. Here the reaction of crystalline lattice on excitation was taken into account. Such consideration leads to nonlinear Schredinger equations. At a solution of these equations some possible variants of the nonlinearities which are different from the cubic are considered. The possibility of constructing of spherically-symmetric analytical solutions with finite norm analyzed. The analytical solutions in the form of centrally symmetric solitons were found. The obtained solutions show the expressed wave-corpuscle dualism. It is shown, that dynamic properties of excitation are identical to dynamics of not self-trapped quasiparticle. An important feature of these solutions is that their amplitudes (or squares of the amplitudes) have an asymptotic behavior of the type of 1/ρ, with ρ →∞.