# Wavefunction: Particle in a 1-dimensional potential Well

1. Oct 1, 2008

### samdiah

1. The problem statement, all variables and given/known data

Find the wave function of particle in a 1-dimensional potential Well of length L, n=2 and mass m

2. Relevant equations

I think this would be the wave equation, but not 100% sure
$$\varphi=Asin(n\pix/L)[\tex] where n=1,2,3... tex doesn't work for me---=Asin[n*pi/L] 3. The attempt at a solution I tried to normalize the function using what the book says and came up with integral of (sin2[n*pi/L]dx[ Is this right? Now I need to find probablity with this....how would I do this? Can someone please tell me if I am on the right footsteps? Any help is appreciated. Last edited: Oct 1, 2008 2. Oct 1, 2008 ### malawi_glenn What do you mean with "I need to find probability with this" ? Probability for what? You have not specified that yet. Try this with tex: [tex]\varphi (x) = A\ sin(n\pi x/L)$$

You may insert n=2 already at this stage.

Then you are on the right track;
$$|A|^2 \int _0^L\varphi ^*(x)\varphi (x) = 1$$
(If you have an INFINITE deep potential well)

So work this integral out, then specify what your probability question is.

3. Oct 1, 2008

### quantumech

Thanks. Ok for the probablity we have this mass m in length of box L with state n=2. we r suppose to calculate probablity for 1st half of the box. I know i have to take integral of half the box from 0 to l/2 but not sure how.

4. Oct 1, 2008