## Abstract

We prove an uncertainty relation for energy and arrival time, where the arrival of a particle at a detector is modeled by an absorbing term added to the Hamiltonian. In this well-known scheme the probability for the particles arrival at the counter is identified with the loss of normalization for an initial wave packet. Under the sole assumption that the absorbing term vanishes on the initial wavefunction, we show that ΔTΔE ≥ √ ph and , where 〈T〉 denotes the mean arrival time and p is the probability for the particle to be eventually absorbed. Nearly minimal uncertainty can be achieved in a two-level system, and we propose a trapped ion experiment to realize this situation.

Original language | English |
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Article number | 185301 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 45 |

Issue number | 18 |

DOIs | |

Publication status | Published - 19 Apr 2012 |

Externally published | Yes |