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Spectral Analysis of a Complex Schrödinger Operator in the Semiclassical Limit

2016; Society for Industrial and Applied Mathematics; Volume: 48; Issue: 4 Linguagem: Inglês

10.1137/15m1047222

1095-7154

Yaniv Almog, Raphaël Henry,

Numerical methods in inverse problems

We consider the Dirichlet realization of the operator $-h^2\Delta+iV$ in the semiclassical limit $h\to0$, where $V$ is a smooth real potential with no critical points. For a one-dimensional setting, we obtain the complete asymptotic expansion, in powers of $h$, of each eigenvalue. In two dimensions we obtain the left margin of the spectrum, under some additional assumptions.