A duality between Schrödinger operators on graphs and certain Jacobi matrices
P. Exner (1997)
Annales de l'I.H.P. Physique théorique
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P. Exner (1997)
Annales de l'I.H.P. Physique théorique
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Zhongwei Shen (1996)
Journées équations aux dérivées partielles
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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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Stepan Manko (2014)
Mathematica Bohemica
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In 1986 P. Šeba in the classic paper considered one-dimensional pseudo-Hamiltonians containing the first derivative of the Dirac delta function. Although the paper contained some inaccuracy, it was one of the starting points in approximating one-dimension self-adjoint couplings. In the present paper we develop the above results to the case of quantum systems with complex geometry.
Bernard Helffer, Heinz Siedentop (1995)
Mathematische Zeitschrift
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Udrişte, C., Balan, V., Udrişte, A. (1999)
APPS. Applied Sciences
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