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MaPhySto
The Danish National Research Foundation:
Network in Mathematical Physics and Stochastics



Funded by The Danish National Research Foundation
Seminar
Friday, 31 October 2003, at 13:15 in Fysisk Auditorium
Reinhard Werner
Institute for Mathematical Physics, TU- Braunschweig, Germany
A proof of Heisenberg's first uncertainty relation
Joint MaPhySto - QUANTOP Seminar Joint MaPhySto - QUANTOP Seminar

Abstract
In his famous 1927 paper, Heisenberg introduces two quite distinct aspects of quantum uncertainty. First, the impossibility of performing a precise joint measurement of canonically conjugate observables and second the impossibility of preparing states, in which two conjugate observables both have sharp distributions. While a rigorous statement of the second aspect has become basic textbook material, the first aspect is usually treated only by qualitative discussion. Here we prove a completely general inequality $\delta P \delta Q > C$, with a precise definition of the $\delta$ quantities, expressing the constraint on joint or successive measurements of $Q$ and $P$, and determine the optimal constant $C$.

Contact person:Ole E. Barndorff-Nielsen.