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- W2949557102 abstract "We consider a self-adjoint two-dimensional Schrodinger operator $H_{alphamu}$, which corresponds to the formal differential expression [ -Delta - alphamu, ] where $mu$ is a finite compactly supported positive Radon measure on ${mathbb R}^2$ from the generalized Kato class and $alpha >0$ is the coupling constant. It was proven earlier that $sigma_{rm ess}(H_{alphamu}) = [0,+infty)$. We show that for sufficiently small $alpha$ the condition $sharpsigma_{rm d}(H_{alphamu}) = 1$ holds and that the corresponding unique eigenvalue has the asymptotic expansion $$ lambda(alpha) = -(C_mu + o(1))expBig(-tfrac{4pi}{alphamu({mathbb R}^2)}Big), qquad alpharightarrow 0+, $$ with a certain constant $C_mu > 0$. We obtain also the formula for the computation of $C_mu$. The asymptotic expansion of the corresponding eigenfunction is provided. The statements of this paper extend Simon's results, see cite{Si76}, to the case of potentials-measures. Also for regular potentials our results are partially new." @default.
- W2949557102 created "2019-06-27" @default.
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- W2949557102 date "2014-02-17" @default.
- W2949557102 modified "2023-09-27" @default.
- W2949557102 title "Weakly coupled bound state of 2D Schrodinger operator with potential-measure" @default.
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- W2949557102 hasPublicationYear "2014" @default.
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