ISSN:
1432-0916
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract: We investigate nodal sets of magnetic Schrödinger operators with zero magnetic field, acting on a non simply connected domain in ℝ2. For the case of circulation 1/2 of the magnetic vector potential around each hole in the region, we obtain a characterisation of the nodal set, and use this to obtain bounds on the multiplicity of the groundstate. For the case of one hole and a fixed electric potential, we show that the first eigenvalue takes its highest value for circulation 1/2.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002200050599