Semiclassical analysis of Schrödinger operators with coulomb-like singular potentials

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概要

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• In this paper, we study the behavior of eigenvalues and eigenfunctions of Schrodinger operators whose potentials have finitely many negative singularities. We prove that if potentials behave like $O(|x-p_i|^{-ρ})(0<ρ<2)$ near singular points $x=p_i$, then eigenvalues behave like $O(h^{-\frac{2ρ}{2-ρ}})$ when the Planck constant $h$ approaches to zero. Then we obtain the asymptotic expansion of the eigenvalues and eigenfunctions in $h$. We also study the splitting of the lowest eigenvalues and show that the asymptotic is estimated by a suitable Riemann metric called Agmon distance.

• 東京大学の論文

著者

• Nakano F

  Japan Atomic Energy Res. Inst. Kyoto Jpn

• Nakano Fumihiko

  Department of Mathematical Sciences, University of Tokyo

関連論文

• Semiclassical analysis of Schrödinger operators with coulomb-like singular potentials

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