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Normalization of a wavefunction problem

  • #1

Homework Statement


Normalize sin ((n*pi*x)/L) where x is between 0 and L and n is a positive integer


Homework 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?


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
 

Answers and Replies

  • #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.
 
  • #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?
 
  • #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.
 
  • #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.
 
  • #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...)
 
  • #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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