Time of arrival operator on the circle. (Variations on two Mielnik's works)
Abstract
Using the orthodox Weyl -- Wigner -- Stratonovich -- Cohen (WWSC) quantization rule we construct a time -- of -- arrival operator for a free particle on the circle. It is shown that this operator is self -- adjoint but the careful analysis of its properties suggests that it cannot represent a `physical' time -- of -- arrival observable. The problem of a time -- of -- arrival observable for the `waiting screen' is also considered. A method of avoiding the quantum Zeno effect is proposed and the positive operator valued measure (POV -- measure) or the generalized positive operator valued measure (GPOV -- measure) describing quantum time -- of -- arrival observable for the waiting screen are found.
Keywords
Cite
@article{arxiv.1203.4146,
title = {Time of arrival operator on the circle. (Variations on two Mielnik's works)},
author = {M. Przanowski and M. Skulimowski and J. Tosiek},
journal= {arXiv preprint arXiv:1203.4146},
year = {2013}
}
Comments
7 pages; a talk presented at the XXX Workshop on Geometric Methods in Physics, Bialowieza, Poland, 2011