Wavefunction: Particle in a 1-dimensional potential Well

[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
[tex]\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.

[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:

\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.

[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.

[buffordboy23]

As you probably already know, you will have to compute the integral of a sine-squared term. Here is a link that will have the info you need:

http://en.wikipedia.org/wiki/List_of_integrals_of_trigonometric_functions