(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that the probability of obtaining E_{n}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

|c_{n}|^{2}= 240/(n^{6}[itex]\pi[/itex]^{6})[1-(-1)^{n}]^{2}

2. Relevant equations

c_{n}= [itex]\int[/itex][itex]\psi[/itex][itex]^{*}_{n}[/itex][itex]\Psi[/itex](x)dx

The probability is c_{n}squared.

Shouldn't have to use eigenvalues and eigenfunctions.

3. 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Energy State Probability Particle in a Box

**Physics Forums | Science Articles, Homework Help, Discussion**