MICROLOCAL ESTIMATES OF THE STATIONARY SCHRÖDINGER EQUATION IN SEMI-CLASSICAL LIMIT by

Analytic Smoothing Effect for the Schrödinger Equation with Long-Range Perturbation

We study microlocal analytic singularity of solutions to Schrödinger equation with analytic coefficients. Using microlocal weight estimate developped for estimating the phase space tunneling, we prove microlocal smoothing estimates that generalize results by L. Robbiano and C. Zuily. We suppose the Schrödinger operator is a long-range type perturbation of the Laplacian, and we employ positive c...

On the Semi-classical Limit for the Nonlinear Schrödinger Equation

We review some results concerning the semi-classical limit for the nonlinear Schrödinger equation, with or without an external potential. We consider initial data which are either of the WKB type, or very concentrated as the semi-classical parameter goes to zero. We sketch the techniques used according to various frameworks, and point out some open problems.

Existence and Semi–Classical Limit of the Least Energy Solution to a Nonlinear Schrödinger Equation with Electromagnetic Fields

Semiclassical Limit of the Nonlinear Schrödinger-Poisson Equation with Subcritical Initial Data

We study the semi-classical limit of the nonlinear Schrödinger-Poisson (NLSP) equation for initial data of the WKB type. The semi-classical limit in this case is realized in terms of a density-velocity pair governed by the Euler-Poisson equations. Recently we have shown in [ELT, Indiana Univ. Math. J., 50 (2001), 109–157], that the isotropic Euler-Poisson equations admit a critical threshold ph...

Hydrogen Abstraction Reaction of Hydroxyl Radical with 1,1-Dibromoethane and 1,2-Dibromoethane Studied by Using Semi-Classical Transition State Theory

The hydrogen abstraction reaction by OH radical from CH2BrCH2Br (R1) and CH₃CHBr2 (R2) is investigated theoretically by semi-classical transition state theory. The stationary points for both reactions are located by using ωB97X-D and KMLYP density functional methods along with cc-pVTZ basis. Single-point energy calculations are performed at the QCISD(T) and CCSD(T) levels of theory with differe...