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Homework Help: Normalization of a wavefunction problem

  1. Jan 19, 2010 #1
    1. The problem statement, all variables and given/known data
    Normalize sin ((n*pi*x)/L) where x is between 0 and L and n is a positive integer


    2. Relevant equations
    integral (psi*psi)dx=1
    N^2 integral sin ((n*pi*x)/L)dx =1

    I don't really understand if this integral is correct, what is the complex conjugate of the wavefunction?

    Can i just integrate my wavefunction and say tht is psi*psi?


    3. The attempt at a solution
    N^2 integral sin ((n*pi*x)/L)dx =1

    -N^2 Lcos ((n*pi*x/L))/n*pi=1
    I just integrated the wavefunction and then solved for N
     
  2. jcsd
  3. Jan 19, 2010 #2

    Matterwave

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    The complex conjugate of a real number or function is just that number/function itself. You should be squaring your function. You can't just integrate your function alone, it has to be multiplied by itself.
     
  4. Jan 19, 2010 #3
    Ohh, thanks! I was very confused.
    So then I would square my function and then integrate and solve for N?
    then my normalized wavefunction would be N times the original function?
     
  5. Jan 19, 2010 #4

    Matterwave

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    Yes. I don't know why you have a N squared though. There's no reason for N to be squared. N is just some as yet undetermined constant. Squaring it will just confuse you.
     
  6. Jan 19, 2010 #5

    vela

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    The usual way it's done is you write

    [tex]\psi_n(x) = N \sin{\left(\frac{n\pi x}{L}\right)[/tex]

    where N is the yet unknown normalization constant. Then you plug this wavefunction into

    [tex]1=\int_0^L \psi_n^*(x)\psi_n(x) dx[/tex]

    and solve for N. Since both [itex]\psi_n^*(x)[/itex] and [itex]\psi_n(x)[/itex] contain N, you get [itex]N^2[/itex] in the equation.
     
  7. Jan 19, 2010 #6

    Matterwave

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    Ah right, it's been a while...I suppose N^2 would be appropriate. Otherwise, you'd square-root N. (I always use A instead of N which adds to my confusion...)
     
  8. Jan 19, 2010 #7
    Sorry about that, i just saw it in my textbook and copied it down, but Vela's explanation really cleared it up! thanks both of you guys. Sorry im a newbie when it comes to this stuff... and i'm rusty on math.

    Also would you guys know anything about guassian integrals? if i was trying to integrate e^(-2ax^2)?
     
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