Determine the probability that a particle in 1-dimension box of length a, with no forces acting on it, in state corresponding to n=10,will be found in the region between a/3 and 2a/3.

Explanation:

The probability to find a particle in a 1 dimension box of length is:

Let's recall the wave function of a particle in this candiction will be:

So the propability:

Solving the integral, it is:

We can cancel out a and using n = 10, the probabilty finally will be:

I hope it helps you!