Time of arrival operator on the circle. (Variations on two Mielnik's works)

Details Time of arrival operator on the circle. (Variations on two Mielnik's works) Time of arrival operator on the circle. (Variations on two Mielnik's works)

2012-03-19

arxiv.org/abs/1203.4146v1

Physics

Quantum Physics

7 pages; a talk presented at the XXX Workshop on Geometric Methods in Physics, Bialowieza, Poland, 2011

Scientific paper

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.

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