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Wavefunction: Particle in a 1-dimensional potential Well

  1. Oct 1, 2008 #1
    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.
     
    Last edited: Oct 1, 2008
  2. jcsd
  3. Oct 1, 2008 #2

    malawi_glenn

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    Science Advisor
    Homework Helper

    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) [/tex]

    You may insert n=2 already at this stage.

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

    So work this integral out, then specify what your probability question is.
     
  4. Oct 1, 2008 #3
    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.
     
  5. Oct 1, 2008 #4
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