Shu Nakamura

We consider the scattering theory for discrete Schr\&quot;odinger operators on<br />
with long-range potentials. We prove the existence of modified wave<br />
operators constructed in terms of solutions of a Hamilton-Jacobi equation on<br />...

In a previous paper by the second author [11], we discussed a characterization of the microlocal singularities for solutions to Schrodinger equations with long range type perturbations, using solutions to a Hamilton-Jacobi equation. In this paper ...

The object of study in this paper is the on-shell scattering matrix S(E) of the Schrodinger operator with the potential satisfying assumptions typical in the theory of shape resonances. We study the spectrum of S(E) in the semiclassical limit when...

On this short note, we apply the Mourre theory of the limiting absorption<br />
with {\it difference} type conditions on the potential, instead of conditions<br />
on the derivatives. In order that we modify the definition of the conjugate<br />
o...