Homework Help: 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