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Displaying similar documents to “On the spectrum and eigenfunctions of the Schrödinger operator with Aharonov–Bohm magnetic field.”

Dynamical Resonances and SSF Singularities for a Magnetic Schrödinger Operator

Astaburuaga, María Angélica, Briet, Philippe, Bruneau, Vincent, Fernández, Claudio, Raikov, Georgi (2008)

Serdica Mathematical Journal

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We consider the Hamiltonian H of a 3D spinless non-relativistic quantum particle subject to parallel constant magnetic and non-constant electric field. The operator H has infinitely many eigenvalues of infinite multiplicity embedded in its continuous spectrum. We perturb H by appropriate scalar potentials V and investigate the transformation of these embedded eigenvalues into resonances. First, we assume that the electric potentials are dilation-analytic with respect to the variable...

Asymptotic distribution of negative eigenvalues for two dimensional Pauli operators with nonconstant magnetic fields

Akira Iwatsuka, Hideo Tamura (1998)

Annales de l'institut Fourier

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This article studies the asymptotic behavior of the number N ( λ ) of the negative eigenvalues < - λ as λ + 0 of the two dimensional Pauli operators with electric potential V ( x ) decaying at and with nonconstant magnetic field b ( x ) , which is assumed to be bounded or to decay at . In particular, it is shown that N ( λ ) = ( 1 / 2 π ) V ( x ) > λ b ( x ) d x ( 1 + o ( 1 ) ) , when V ( x ) decays faster than b ( x ) under some additional conditions.