2 6 Ja n 20 04 Scattering Theory for the Schrödinger Equation in some External Time Dependent Magnetic Fields

Scattering and Trapping of Nonlinear Schrödinger Solitons in External Potentials

Soliton motion in some external potentials is studied using the nonlinear Schrödinger equation. Solitons are scattered by a potential wall. Solitons propagate almost freely or are trapped in a periodic potential. The critical kinetic energy for reflection and trapping is evaluated approximately with a variational method. keywords: soliton, nonlinear Schrödinger equation, Lagrangian The nonlinea...

Ja n 20 04 Schrödinger equation with critical Sobolev exponent

ua nt - p h / 99 11 09 3 v 3 2 1 Ja n 20 02 SCHRÖDINGER EQUATIONS WITH TIME - DEPENDENT

We present some general results for the time-dependent mass Hamiltonian problem with H = − 2e∂xx + h(2)(t)e2ν(t)x2, where ν(t) is a continuous function of t. This Hamiltonian corresponds to a time-dependent mass (TM) Schrödinger equation with the restriction that there are only P 2 and X2 terms. We give the specific transformations to a different quadratic Schrödinger(TQ) equation and to a diff...

Strichartz Estimates for the Magnetic Schrödinger Equation

We prove global, scale invariant Strichartz estimates for the linear magnetic Schrödinger equation with small time dependent magnetic field. This is done by constructing an appropriate parametrix. As an application, we show a global regularity type result for Schrödinger maps in dimensions n ≥ 6.

Properties of the Schrödinger Theory of Electrons in Electromagnetic Fields

The Schrödinger theory of electrons in an external electromagnetic field can be described from the perspective of the individual electron via the ‘Quantal Newtonian’ laws (or differential virial theorems). These laws are in terms of ‘classical’ fields whose sources are quantal expectations of Hermitian operators taken with respect to the wave function. The laws reveal the following physics: (a)...