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

Anders M. Hansson

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-16

Abstract:

We explicitly compute the spectrum and eigenfunctions of the magnetic Schrödinger operator H ( A → , V ) = ( i ∇ + A → ) 2 + V in L 2 ( ℝ 2 ) , with Aharonov-Bohm vector potential, A → ( x 1 , x 2 ) = α ( − x 2 , x 1 ) / | x | 2 , and either quadratic or Coulomb scalar potential V . We also determine sharp constants in the CLR inequality, both dependent on the fractional part of α and both greater than unity. In the case of quadratic potential, it turns out that the LT inequality holds for all γ ≥ 1 with the classical constant, as expected from the nonmagnetic system (harmonic oscillator).

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:313787

DOI: 10.1155/IJMMS.2005.3751

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