What is time in quantum mechanics?

Time of arrival in quantum mechanics is discussed in two versions: the classical axiomatic "time of arrival operator" introduced by Kijowski and the event enhanced quantum theory (EEQT) method. It is suggested that for free particles the two methods may lead to the same result. On the other hand, the EEQT method can be easily geometrized within the framework of Galilei–Newton general relativistic quantum mechanics developed by M. Modugno and collaborators, and it can be applied to non-free evolutions. The way of geometrization of irreversible quantum dynamics based on dissipative Liouville equation is suggested.