## Semi-classical states for non-self-adjoint Schrödinger operators.(English)Zbl 0921.47060

Summary: We prove that the spectrum of certain non-selfadjoint Schrödinger operators is unstable in the semi-classical limit $$h\to 0$$. Similar results hold for a fixed operator in the high energy limit. The method involves the construction of approximate semiclassical modes of the operator by the JWKB method for energies far from the spectrum.

### MSC:

 47N50 Applications of operator theory in the physical sciences 81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
Full Text: