Wavefunction: Particle in a 1-dimensional potential Well

[samdiah]

Homework Statement

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

Homework Equations

I think this would be the wave equation, but not 100% sure
$$\varphi=Asin(n\pix/L)[\tex] where n=1,2,3...<br /> <br /> tex doesn't work for me---=Asin[n*pi/L]<br /> <br /> <h2>The Attempt at a Solution</h2><br /> <br /> I tried to normalize the function using what the book says and came up with <br /> <br /> integral of (sin²[n*pi/L]dx[<br /> <br /> Is this right? Now I need to find probability with this...how would I do this? Can someone please tell me if I am on the right footsteps?<br /> <br /> Any help is appreciated.$$

 

[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 probability we have this mass m in length of box L with state n=2. we r suppose to calculate probability 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