On the spectrum and eigenfunctions of the Schrödinger operator with Aharonov-Bohm magnetic field
2005 (English)In: International journal of mathematics and mathematical sciences, ISSN 0161-1712, E-ISSN 1687-0425, Vol. 2005, no 23, 3751-3766 p.Article in journal (Refereed) Published
We explicitly compute the spectrum and eigenfunctions of the magnetic Schrödinger operator H (A, V) = (i∇ + A)2 + V in L2(ℝ2), with Aharonov-Bohm vector potential, A(x1,x2) = α(-x2,x1)/ 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).
Place, publisher, year, edition, pages
2005. Vol. 2005, no 23, 3751-3766 p.
IdentifiersURN: urn:nbn:se:kth:diva-7813DOI: 10.1155/IJMMS.2005.3751OAI: oai:DiVA.org:kth-7813DiVA: diva2:12947
QC 201007122007-12-122007-12-122010-07-12Bibliographically approved