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.


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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