About conditional probabilities of events regarding the quantum mechanical measurement process
Year: 2006
Type: preprint
Abstract: We consider successive measurements of position and momentum of a single particle. Let P be the conditional probability to measure the momentum k with accuracy ∆k, given a previously successful position measurement q with accuracy ∆q. Several upper bounds for the probability P are determined. For arbitrary, but given accuracies ∆q, ∆k, these bounds refer to the variation of q, k, the state vector ψ of the particle as well as to an infinite set of measuring partitions. A simple bound is given by the inequality P ≤ ∆k∆q h, where h is Planck’s quantum of action. It is nontrivial for all measurements with ∆k∆q < h. The second bound is obtained by considering the Hilbert-Schmidt norm. As our main result the least upper bound of P is determined. All bounds are independent of the order with which the measuring of position and momentum is made.
Author: Thomas Schürmann
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2144252007