1. The problem statement, all variables and given/known data A particle is in the first excited state of a box of length L. Find the probability of finding the particle in the interval ∆x = 0.007L at x = 0.55L. 2. Relevant equations P = ∫ ψ*ψdx from .543L to .557L 3. The attempt at a solution Normalizing ψ gives ψ=√(2/L)sin(nπx/L) P = ∫ ψ*ψdx = ∫(2/L)sin^2(nπx/L)dx from .543L to .557L The integration simplifies to P = x/L - sin(4πx/L)/4 so P = [.557L/L - sin(4π*.557L/L)/4] - [.543L/L - sin(4π*.543L/L)/4] P = 0.0132 or 1.32% This is wrong though and the hint given afterwords was that because the Δx is so small, there is no need for integration. This just confuses me because abs(ψ)^2 will have a 1/L factor in it. Any help will be useful. Thanks!