No abstract

A three-dimensional soliton model of photon with corpuscular and wave properties is proposed. We consider the Maxwell equations and assume that light induces the polarization and magnetization of vacuum only along the direction of its propagation. The nonlinear equation constructed for the vector potential is similar to the generalized nonlinear Schrödinger equation and comprises a dimensionless constant μ that determines the size-scale of soliton and is expected to be small. The obtained one-soliton solution of the proposed nonlinear equation describes a three-dimensional object identified as photon.

We investigate many characteristic features of revival and fractional revival phenomena via derived analytic expressions for an autocorrelation function of a one-dimensional Rydberg atom with weighting probabilities modelled by a Gaussian or a Lorentzian distribution. The fractional revival phenomenon in the ionization probabilities of a one-dimensional Rydberg atom irradiated by two short half-cycle pulses is also studied. When many states are involved in the formation of the wave packet, the revival is lower and broader than the initial wave packet and the fractional revivals overlap and disappear with time.

The form factor for the transition between the hydrogenic states with parabolic quantum numbers n 1 n 2 m and n 1 Јn 2 ЈmЈ is obtained in a closed analytic form. The asymptotic limit of the transition form factor at large parabolic quantum numbers is derived, and a comparison with exact quantum calculations shows that the asymptotic limit is accurate in a wide region of parabolic quantum numbers and the momentum p transferred to electrons. A simple quasiclassical formula for the transition probability is given, and the range of quantum numbers corresponding to quasiclassically forbidden transitions are defined.

The previously proposed three-dimensional soliton model of a photon propagating in vacuum is modified to describe its propagation in a homogeneous linear dielectric medium. The one-soliton solution of the derived nonlinear equation correctly predicts the energy and the Abraham and Minkowski momenta of the photon in dielectrics. A new nonlinear equation is proposed, which has a one-soliton solution that at every point oscillates with the same frequency and falls exponentially in the longitudinal, as well as in the transverse direction from the centre of the soliton.