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On the location of resonances for Schrödinger operators in the semiclassical limit. I: Resonances free domains. (English) Zbl 0629.47043

One shows that in the semi-classical regime and under suitable non- trapping conditions on the potential V at energy E of Virial relation type: \(2(V-E)+x\nabla V<0\) the Schrödinger operator \(H-\hslash^ 2\Delta +V\) has no resonances in some complex neighbourhood of E.
Some critical values of E like thresholds or barrier tops are also discussed.

MSC:

47F05 General theory of partial differential operators
47A10 Spectrum, resolvent
35J10 Schrödinger operator, Schrödinger equation
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