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The main object of this paper is to analyze the recent results obtained on the Neumann realization of the Schrödinger operator in the case of dimension 3 by Lu and Pan. After presenting a short treatment of their spectral analysis of keymodels, we show briefly how to implement the techniques of Helffer-Morame in order to give some localization of the ground state. This leaves open the question of the localization by curvature effect which was solved in the case of dimension 2 in our previous work and will be analysed in the case of dimension 3 in a future paper. 相似文献
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We consider a magnetic Laplacian −Δ
A
= (id + A)* (id + A) on a non-compact hyperbolic surface M with finite area. A is a real one-form and the magnetic field dA is constant in each cusp. When the harmonic component of A satisfies some quantified condition, the spectrum of −Δ
A
is discrete. In this case, we prove that the counting function of the eigenvalues of −Δ
A
satisfies the classical Weyl formula, even when dA=0. 相似文献
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