# Exact quantum-mechanical propagator for an electron in a saddle-point potential and a magnetic field

Damme van, Ruud and Wiegel, Frederik W. and Harrison, Michael J. (1989) *Exact quantum-mechanical propagator for an electron in a saddle-point potential and a magnetic field.* Physical review B: Condensed matter, 39 (6). pp. 3780-3784. ISSN 0163-1829

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Abstract: | We study the time-dependent propagator for an electron which moves in a plane and which is subject to quadrupolar electric fields with certain reflection symmetries, and to a uniform magnetic field perpendicular to the plane. It is shown that the electric potential, which has a saddle point at the origin, can be produced by voltages applied to four symmetrically configured cylindrical electrodes whose axes are perpendicular to the plane. We use path-integral methods to derive a closed-form expression for the propagator, and comment in some detail on the structure of its normalization factor. |

Item Type: | Article |

Copyright: | © 1989 Institute of Physics |

Faculty: | Electrical Engineering, Mathematics and Computer Science (EEMCS) |

Research Group: | |

Link to this item: | http://purl.utwente.nl/publications/61295 |

Official URL: | http://dx.doi.org/10.1103/PhysRevB.39.3780 |

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Metis ID: 129083