Write down and sketch the probability distribution for the second excited state (n=3) of a particle in a rigid box of length a.
What are the probabilities of finding a particle in the intervals [0.50a, 0.51a] and [0.75a, 0.76a]?
|ψ(x)|^2 = (2/L)sin^2(n∏x/L)
The Attempt at a Solution
I've found the solution online: http://www.uic.edu/classes/phys/phys244ma/p244hw7.html
However, I'm not understanding how they are getting the answers.
Multiply the wave-function squared times the distance between the two points, but I'm not sure why the sine squared term in the first part is one, while in the second part you are to use sin^2(9∏/4)?