Energy and time in simultaneous measurements of position and momentum

Institut für Quantenphysik, Universität Ulm - D-89069 Ulm, Germany, EU

Received: 25 July 2011
Accepted: 23 September 2011

Abstract

The prototype of a simultaneous measurement of position and momentum of a quantum particle was originally introduced by Arthurs and Kelly in 1965. It relies on coupling a quantum particle to two additional systems, which serve as measurement pointers. In this contribution, we start from the question for optimal pointers for such a setup. This allows us to identify a particular readout time with the help of a suitably chosen preparation energy of the measurement apparatus. Hence we find a natural connection between energy and time in a simultaneous measurement concept. Finally, our analysis sheds new light onto the distinctive role played by coherent states in quantum physics.