Exploring Quantum Physics - Week 3 Extra Credit Question 5 - Final Part 5

Reaching the end of Question 5 - we will conclude with the answer.

These are the correct choices:

• $X(t) \leq L$
• $P(t) = 0$
• $\frac{\partial P^2(t)}{\partial t} = 0$
• $\frac{\partial P(t)}{\partial t} = 0$
• $\frac{\partial X(t)}{\partial t} = 0$

And this is not

• $X(t) = 0$

Looking in retrospect, I don't have to compute all those moments. All of these can be argued without derivation at all. First of all, of course it makes sense the particle stay within the well. Second option is not obvious, but if the particle take an average drift, the probability density would not be stationary. The rest are just the fact that the probability density is stationary and therefore have no relation to $ t $. 

The wrong one is simply ridiculous. How could the particle has an average position of 0?