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Using the orthodox Weyl -- Wigner -- Stratonovich -- Cohen (WWSC)quantization rule we construct a time -- of -- arrival operator for a freeparticle on the circle. It is shown that this operator is self -- adjoint butthe 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 ofavoiding the quantum Zeno effect is proposed and the positive operator valuedmeasure (POV -- measure) or the generalized positive operator valued measure(GPOV -- measure) describing quantum time -- of -- arrival observable for thewaiting screen are found.

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