The Fate of the Landau Levels under Perturbations of Constant Sign
نویسندگان
چکیده
We show that the Landau levels cease to be eigenvalues if we perturb the 2D Schrödinger operator with constant magnetic field, by bounded electric potentials of fixed sign. We also show that, if the perturbation is not of fixed sign, then any Landau level may be an eigenvalue of the perturbed problem. AMS 2000 Mathematics Subject Classification: 35J10, 81Q10, 35P20
منابع مشابه
1 4 Ja n 20 09 The Fate of the Landau Levels under Perturbations of Constant Sign July 19 , 2009
We show that the Landau levels cease to be eigenvalues if we perturb the 2D Schrödinger operator with constant magnetic field, by bounded electric potentials of fixed sign. We also show that, if the perturbation is not of fixed sign, then any Landau level may be an eigenvalue of arbitrary, finite or infinite, multiplicity of the perturbed problem. AMS 2000 Mathematics Subject Classification: 35...
متن کاملThe Fate of the Landau Levels under Perturbations of Constant Sign July 1 , 2009
We show that the Landau levels cease to be eigenvalues if we perturb the 2D Schrödinger operator with constant magnetic field, by bounded electric potentials of fixed sign. We also show that, if the perturbation is not of fixed sign, then any Landau level may be an eigenvalue of the perturbed problem. AMS 2000 Mathematics Subject Classification: 35J10, 81Q10, 35P20
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