Schrodinger Wave Equation

Schrodinger equation and wave equation on finite graphs

Abstract. In this paper, we study the schrodinger equation and wave equation with the Dirichlet boundary condition on a connected finite graph. The explicit expressions for solutions are given and the energy conservations are derived. Applications to the corresponding nonlinear problems are indicated. Mathematics Subject Classification 2000: 53Cxx,35Jxx

Inverse Schrodinger equation and the exact wave function

On the wave operators for the critical nonlinear Schrodinger equation

We prove that for the L-critical nonlinear Schrödinger equations, the wave operators and their inverse are related explicitly in terms of the Fourier transform. We discuss some consequences of this property. In the onedimensional case, we show a precise similarity between the L-critical nonlinear Schrödinger equation and a nonlinear Schrödinger equation of derivative type.

Schrodinger Equation and Quantum Chemistry

Collapse Turbulence in Nonlinear Schrodinger Equation

Abstract. We consider a nonlinear Schrodinger equation (NLS) with dissipation and forcing in critical dimension. Without both linear and nonlinear dissipation NLS results in a flnite-time singularity (collapse) for any initial conditions. Dissipation ensures collapse regularization. If dissipation is small then multiple near-singular collapses are randomly distributed in space and time forming ...