A particle is in a box of width L. Calculate the probability to find the particle in the region [L/4, 3L/4] when the particle is a) in the ground state b) in the first excited state.
(2/L)sin(n*π*x/L)^2 dx is the probability in [x, x+dx]
The Attempt at a Solution
Integrating that gives me 2/L[x/2-[L/(4π)]sin(2n*π*x/L)], boundaries being L/4 and 3L/4. For a) n=1 and b) n=2, right? After I plug in the values, I get value greater than 1. Where have I gone wrong?
Hopefully this is readable, no LaTeX.