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 ‘waitingscreen ’ is also considered. A method of avoidingthe quantum Zeno effect is proposed and the positive operator-valued measure (POV-measure) or the generalized positive operator-valued measure (GPOV-measure) describingq uantum time of arrival observable for the waitings creen are found.
Mathematics Subject Classification (2010). Primary 81S05; Secondary 81P15.
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Przanowski, M., Skulimowski, M., Tosiek, J. (2013). A Time of Arrival Operator on the Circle (Variations on Two Ideas). In: Kielanowski, P., Ali, S., Odzijewicz, A., Schlichenmaier, M., Voronov, T. (eds) Geometric Methods in Physics. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0448-6_21
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