Davies, E. B. Semi-classical states for non-self-adjoint Schrödinger operators. (English) Zbl 0921.47060 Commun. Math. Phys. 200, No. 1, 35-41 (1999). 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. Cited in 3 ReviewsCited in 47 Documents MSC: 47N50 Applications of operator theory in the physical sciences 81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory Keywords:spectrum; non-selfadjoint Schrödinger operators; semi-classical limit; high energy limit; approximate semiclassical modes; JWKB method; energies far from the spectrum × Cite Format Result Cite Review PDF Full Text: DOI arXiv