### Abstract

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-δ}) 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.

Original language | English |
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Pages (from-to) | 103-114 |

Number of pages | 12 |

Journal | Letters in Mathematical Physics |

Volume | 50 |

Issue number | 2 |

DOIs | |

Publication status | Published - Oct 2 1999 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Letters in Mathematical Physics*,

*50*(2), 103-114. https://doi.org/10.1023/A:1007679721268

**Anomalous Pauli electron states for magnetic fields with tails.** / Exner, P.; Hirokawa, M.; Ogurisu, O.

Research output: Contribution to journal › Article

*Letters in Mathematical Physics*, vol. 50, no. 2, pp. 103-114. https://doi.org/10.1023/A:1007679721268

}

TY - JOUR

T1 - Anomalous Pauli electron states for magnetic fields with tails

AU - Exner, P.

AU - Hirokawa, M.

AU - Ogurisu, O.

PY - 1999/10/2

Y1 - 1999/10/2

N2 - 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-δ) 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.

AB - 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-δ) 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.

UR - http://www.scopus.com/inward/record.url?scp=0007376244&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0007376244&partnerID=8YFLogxK

U2 - 10.1023/A:1007679721268

DO - 10.1023/A:1007679721268

M3 - Article

AN - SCOPUS:0007376244

VL - 50

SP - 103

EP - 114

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 2

ER -