  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.
