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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
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