Mathematics and Statistics Vol. 2(2), pp. 101 - 104
DOI: 10.13189/ms.2014.020206
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Some Remarks on the Spectrum of the Magnetic Stark Hamiltonians

Rachid Assel ¹, Mouez Dimassi ^2,*, Claudio Fernandez ^3
1 Département de Mathématiques, Université des Sciences de Monastir, 5019 Monastir, Tunisie
² Université Bordeaus I, Institute de Mathématiques de Bordeaux, 351, Cours de Lalibération, 33405 Talence, France
³ Universidad Catolica de Chile

ABSTRACT

The main purpose of this note is to study spectral properties of the Stark magnetic Hamiltonian : , on the Hilbert space L²(R²). We show that if the potential V satisfies some mild regularity conditions and is sufficiently decaying at infinity, then the operator H(μ, ϵ) has possibly at most a finite number of eigenvalues.

KEYWORDS
Embedded Eigenvalue, Magnetic, Stark Hamiltonian, Semi-classical Parametrix

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Rachid Assel , Mouez Dimassi , Claudio Fernandez , "Some Remarks on the Spectrum of the Magnetic Stark Hamiltonians," Mathematics and Statistics, Vol. 2, No. 2, pp. 101 - 104, 2014. DOI: 10.13189/ms.2014.020206.

(b). APA Format:
Rachid Assel , Mouez Dimassi , Claudio Fernandez (2014). Some Remarks on the Spectrum of the Magnetic Stark Hamiltonians. Mathematics and Statistics, 2(2), 101 - 104. DOI: 10.13189/ms.2014.020206.