Well, the Schrödinger equation only describes the evolution of the wavefunction over time (which is indeed a similarity with classical mechanics). But how the w

Well, the Schrödinger equation only describes the evolution of the wavefunction over time (which is indeed a similarity with classical mechanics). But how the wavefunction then further relates to the actual "state of system" is up to the interpretations of quantum mechanics. And there in lies my point: That because of the superposition the way time works in quantum mechanics (properties are simultaneously in a combination of states) is very different from classical mechanics (properties are in exactly one state at a time), even if both have a "t" in their equations. > For example, in classical mechanics you cannot rotate in a way that makes the time coordinate fall in a space coordinate, while you can do that in relativity That is a good point. Maybe it is fair to say that in classical mechanics we start out with an additional separate geometric dimension (which only translation / shifting is allowed in). And in special relativity it gets promoted to a full spacial dimension, allowing all sorts of transformations.