I was learning Basic Quantum mechanics. I cam across the fluid equation in QM, which suggests $\Psi^*\Psi$ is probability density function.
Consider the two statements below
- Probability will change with time. If probability of finding a particle at one place os increased, then the probability of finding this particle in some other place is decreased. So,we can define a probability flow, which gave the continue equation in QM.
- If wave function is normalised once to one. It can be derived that the wave function is normalised for ever. Means, it's independent of time.
As per 2nd statement probability is independent of time and as first, probability is dependent of time. What is actually correct? Or is that implies that we can't apply continue equation, once it's normalised?