What is the probability, P, of locating a particle between x = 0 (the left-hand end of
a box) and x = 0.2 nm in its lowest energy state in a box of length 1.0 nm?
Probability = ∫ψ2dx
ψ = (2/L)1/2sin(n∏x)
The Attempt at a Solution
ψ2 = (2/L)sin2(n∏x)
∫(2/L)sin2(n∏x)dx = 2/L [x/2 - (L/n∏x)sin(2n∏x/L)] from x = 0 to x = 0.2
I plugged in the numbers n=1 and L = 1 and got about 0.2.
The answer is 0.05.