This 1-D Schrödinger equation describes the non relativistic motion of a single charged particle (mass m = 1, = 1) with a potential V in a uniform electric field t → u(t). With v̈ = −u, (1) represents also the dynamics of a particle in a non Galilean frame of absolute position v (see, e.g., [9]). A change of independent variables (t, q) → (t, z) and dependent variable ψ → φ, transform (1) into (...

A generic nonparaxial model for pulse envelopes is presented. Classic Schrödinger-type descriptions of wave propagation have their origins in slowly-varying envelopes combined with a Galilean boost to the local time frame. By abandoning these two simplifications, a picture of pulse evolution emerges in which frame-of-reference considerations and space-time transformations take center stage. A w...

Enlarged planar Galilean symmetry, built of both space-time and field variables and also incorporating the “exotic” central extension is introduced. It is used to describe nonrelativistic anyons coupled to an electromagnetic field. Our theory exhibits an anomalous velocity relation of the type used to explain the Anomalous Hall Effect. The Hall motions, characterized by a Casimir of the enlarge...