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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Victor Ivrii (1991)
Journées équations aux dérivées partielles
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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...
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). ...
George D. Raikov (1994)
Annales de l'I.H.P. Physique théorique
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Victor Ivrii (1987)
Journées équations aux dérivées partielles
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Hansson, Anders M. (2005)
International Journal of Mathematics and Mathematical Sciences
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Akira Iwatsuka, Hideo Tamura (1998)
Annales de l'institut Fourier
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This article studies the asymptotic behavior of the number of the negative eigenvalues as of the two dimensional Pauli operators with electric potential decaying at and with nonconstant magnetic field , which is assumed to be bounded or to decay at . In particular, it is shown that , when decays faster than under some additional conditions.
S.Z: Levendorski (1996)
Mathematische Zeitschrift
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Elliot H. Lieb (1985-1986)
Séminaire Équations aux dérivées partielles (Polytechnique)
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