Exact energy-time uncertainty relation for arrival time by absorption

Jukka Kiukas*, Andreas Ruschhaupt, Piet O. Schmidt, Reinhard F. Werner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (SciVal)


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 languageEnglish
Article number185301
JournalJournal of Physics A: Mathematical and Theoretical
Issue number18
Publication statusPublished - 19 Apr 2012
Externally publishedYes


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