A Singular Critical Potential for the Schrödinger Operator

A Singular Critical Potential For The Schrödinger operator

We construct a potential V on R, smooth away from one pole, and a sequence of quasimodes for the operator −∆+V , which concentrate on this pole. No smoothing effect, Strichartz estimates nor dispersive inequalities hold for the corresponding Schrödinger equation.

Ground State for the Schrödinger Operator with the Weighted Hardy Potential

A Sharp Maximal Function Estimate for Vector-Valued Multilinear Singular Integral Operator

We establish a sharp maximal function estimate for some vector-valued multilinear singular integral operators. As an application, we obtain the $(L^p, L^q)$-norm inequality for vector-valued multilinear operators.

Fourth order real space solver for the time-dependent Schrödinger equation with singular Coulomb potential

We present a novel numerical method and algorithm for the solution of the 3D axially symmetric timedependent Schrödinger equation in cylindrical coordinates, involving singular Coulomb potential terms besides a smooth time-dependent potential. We use fourth order finite difference real space discretization, with special formulae for the arising Neumann and Robin boundary conditions along the sy...

Schrödinger Operators with Singular Potentials †

We describe classical and recent results on the spectral theory of Schrödinger and Pauli operators with singular electric and magnetic potentials