Anomalous Pauli electron states for magnetic fields with tails

Details Anomalous Pauli electron states for magnetic fields with tails Anomalous Pauli electron states for magnetic fields with tails

1999-09-10

arxiv.org/abs/math-ph/9909011v2

Lett. Math. Phys. 50 (1999), 103-114

Physics

Mathematical Physics

12 pages, LaTeX2e; the final version, to appear in Lett. Math. Phys

Scientific paper

10.1023/A:1007679721268

We consider a two-dimensional electron with an anomalous magnetic moment, g>2, interacting with a nonzero magnetic field B perpendicular to the plane which gives rise to a flux F. Recent results about the discrete spectrum of the Pauli operator are extended to fields with the O(r^{-2-\delta}) decay at infinity: we show that if |F| exceeds an integer N, there is at least N+1 bound states. Furthermore, we prove that weakly coupled bound states exist under mild regularity assumptions also in the zero flux case.

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