BRUNEAU, Vincent; MIRANDA, Pablo; RAIKOV, Georgi

doi:10.1142/S0129055X14500032

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BRUNEAU, Vincent
Institut de Mathématiques de Bordeaux [IMB]

MIRANDA, Pablo
Facultad de Matemáticas [Santiago de Chile]

RAIKOV, Georgi
Facultad de Matemáticas [Santiago de Chile]

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Reviews in Mathematical Physics. 2014, vol. 26, n° 2, p. 1450003

World Scientific Publishing

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Let H-0,(D) (respectively, H-0,H-N) be the Schrodinger operator in constant magnetic field on the half-plane with Dirichlet (respectively, Neumann) boundary conditions, and let H-l := H-0,H-l - V, l = D, N, where the scalar potential V is non-negative, bounded, does not vanish identically, and decays at infinity. We compare the distribution of the eigenvalues of H-D and H-N below the respective infima of the essential spectra. To this end, we construct effective Hamiltonians which govern the asymptotic behavior of the discrete spectrum of Hl near inf sigma(ess)(H-l) = inf sigma(H-0,H-l), l = D, N. Applying these Hamiltonians, we show that sigma(disc)(H-D) is infinite even if V has a compact support, while sigma(disc)(H-N) could be finite or infinite depending on the decay rate of V< Réduire

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Dirichlet and Neumann eigenvalues for half-plane magnetic Hamiltonians

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