Spectral analysis of a complex Schr "odinger operator in the\n semiclassical limit

2015/10/22 by Yaniv Almog, Almog, Yaniv, Raphaël Henry +1 · 3 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1510.06806

openalex publication_date 2015/10/22 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We consider the Dirichlet realization of the operator -h²\Δ+iV in the\nsemi-classical limit h\→0, where V is a smooth real potential with no\ncritical points. For a one dimensional setting, we obtain the complete\nasymptotic expansion, in powers of h, of each eigenvalue. In two dimensions\nwe obtain the left margin of the spectrum, under some additional conditions.\n

Cited by

• Localization of the eigenfunctions of a Bloch-Torrey operator on the half-plane
• Weak coupling for Schrödinger operators with complex potentials
• Semiclassical tunneling for some 1D Schrödinger operators with complex-valued potentials

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