Calculating Probability Density in Quantum Mechanics

[Tigersharkmks]

In quantum mechanics, given ψ, we calculate the probability density in a given space by (mod[ψ]^2)*dx*dy*dz (as given in any standard textbook). But my suggetion is that it should be (mod[ψ]^2)*dx*dy*dz*dt where dt is the differential time element. Its seems to me to be more fundamental. Then why don't we do that?
Thanks
Curious undergrad!

 

[mathman]

The probability density is at a given instant, not per unit time.

 

[HallsofIvy]

Also we do NOT use $\Psi$ to calculate the probability density. $\Psi$ is the probability density. The integral, over a space interval, gives the probability that the object is in that space at the given instant.

 

[Matterwave]

@HallsofIvy I think you mean the absolute square of the wave function is the probability density.