The Rajeev–Ranken (RR) model is a Hamiltonian system describing screw-type nonlinear waves of wavenumber k in scalar field theory pseudodual to the 1 + 1D SU(2) principal chiral model. Classically, RR Liouville integrable. Here, we interpret as novel 3D cylindrically symmetric quartic oscillator with an additional rotational energy. quantum has two dimensionless parameters. Upon separating vari...

The dynamics of wave packets in a relativistic Dirac oscillator is compared to that of the Jaynes-Cummings model. The strong spin-orbit coupling of the Dirac oscillator produces the entanglement of the spin with the orbital motion similar to what is observed in the model of quantum optics. The collapses and revivals of the spin which result extend to a relativistic theory our previous findings ...