Does the use of probability in quantum physics rely on our present concept of TIME. Stupid or not?

One of the postulates of Quantum Mechanics (QM) is largely based on the Schrodinger equation which is a partial differential equation in the time and space variables which when solved yields the state vector |Psi> of the system at hand. The wave function Psi(

**r**, t) is obtained from the state function by forming the inner product, i.e. by definition Psi(

**r**, t) = <x, t|Psi>. The square of the magnitude of this function is the probability density. The probability of a particle being found in a particular region of space is found by integrating the probability density over the region in question. The probability will in general be a function of time. Even if it's not its calculated from a differential equation where time is one of the variables and the state function is in general a function of time. But in all cases the wave function itself is a function of time even though the square of the magnitude isn't. So in this way time is very important in quantum mechanics and as such, to put it in your terms, QM relies on it.