Schrödinger operators with complex-valued potentials and no resonances

Details Schrödinger operators with complex-valued potentials and no resonances Schrödinger operators with complex-valued potentials and no resonances

2004-08-26

arxiv.org/abs/math-ph/0408052v1

Physics

Mathematical Physics

9 pages

Scientific paper

In dimension $d\geq 3$, we give examples of nontrivial, compactly supported, complex-valued potentials such that the associated Schr\"odinger operators have no resonances. If $d=2$, we show that there are potentials with no resonances away from the origin. These Schr\"odinger operators are isophasal and have the same scattering phase as the Laplacian on $\Real^d$. In odd dimensions $d\geq 3$ we study the fundamental solution of the wave equation perturbed by such a potential. If the space variables are held fixed, it is super-exponentially decaying in time.

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