The magnetic Schrödinger operator and reverse Hölder class

Zhongwei Shen

Displaying similar documents to “The magnetic Schrödinger operator and reverse Hölder class”

Eigenvalue asymptotics for Schrödinger and Dirac operators with the constant magnetic field and with electric potential decreasing at infinity

Victor Ivrii (1991)

Journées équations aux dérivées partielles

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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...

Resonances of two-dimensional Schrödinger operators with strong magnetic fields

Tuan Duong, Anh (2012)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: 81Q20 (35P25, 81V10). The purpose of this paper is to study the Schrödinger operator P(B,w) = (Dx-By^2+Dy^2+w^2x^2+V(x,y),(x,y) О R^2, with the magnetic field B large enough and the constant w № 0 is fixed and proportional to the strength of the electric field. Under certain assumptions on the potential V, we prove the existence of resonances near Landau levels as B®Ґ. Moreover, we show that the width of resonances is of size O(B^-Ґ). ...

Semiclassical and weak-magnetic-field eigenvalue asymptotics for the Schrödinger operator with electromagnetic potential

George D. Raikov (1994)

Annales de l'I.H.P. Physique théorique

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Estimates for a number of negative eigenvalues of the Schrödinger operator with intensive magnetic field

Victor Ivrii (1987)

Journées équations aux dérivées partielles

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On the spectrum and eigenfunctions of the Schrödinger operator with Aharonov–Bohm magnetic field.

Hansson, Anders M. (2005)

International Journal of Mathematics and Mathematical Sciences

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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 $λ \to + 0$ of the two dimensional Pauli operators with electric potential $V (x)$ decaying at $\infty$ and with nonconstant magnetic field $b (x)$ , which is assumed to be bounded or to decay at $\infty$ . In particular, it is shown that $N (λ) = (1 / 2 π) \int_{V (x) > λ} b (x) d x (1 + o (1))$ , when $V (x)$ decays faster than $b (x)$ under some additional conditions.

The asymptotics for the number of eigenvalue branches for the magnetic Schrödinger operator H - ? W in a gap of H.

S.Z: Levendorski (1996)

Mathematische Zeitschrift

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Bounds on Schrödinger operators and generalized Sobolev type inequalities

Elliot H. Lieb (1985-1986)

Séminaire Équations aux dérivées partielles (Polytechnique)

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