- #1
GrantB
- 22
- 0
Homework Statement
Show that the probability of obtaining En for a particle in a box with wave function
[itex]\Psi[/itex](x) = [itex]\sqrt{\frac{30}{L^{5}}}[/itex](x)(L-x) for 0 < x < L
and [itex]\Psi[/itex](x) = 0 for everywhere else
is given by |cn|2 = 240/(n6[itex]\pi[/itex]6)[1-(-1)n]2
Homework Equations
cn = [itex]\int[/itex][itex]\psi[/itex][itex]^{*}_{n}[/itex][itex]\Psi[/itex](x)dx
The probability is cn squared.
Shouldn't have to use eigenvalues and eigenfunctions.
The Attempt at a Solution
I used the integral from (2) and used the given uppercase Psi and used the sqrt(2/L)sin(n*pi*x/L) lowercase psi (conjugate), from 0 to L.
The integral quickly turned messy with integration by parts and such.
I would like to know if I am on the right track here... If I am, I will just work through the integral until I get the right answer.
I'm hoping there is a much easier way to do this.
Thanks!
P.S. Sorry this is a repost from another section. I wasn't getting any responses from the Intro Physics section so thought I would try here.