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Two-Particle Normalization

  1. Dec 10, 2008 #1
    1. The problem statement, all variables and given/known data

    Hi, I've been working on this for a while but I just can't seem to figure this out. I have to solve a problem regarding a one-dimensional two-particle wavefunction psi(x1, x2, t) that is normalized at t=0, and the particles are not in spin. I have to show that the wavefunction remains normalized for all time. I would appreciate any help.

    3. The attempt at a solution

    I know that to normalize, Integral[|psi(x1, x2, t)|^2] =1. So, I have written out the wavefunction, how I think it is, for a two particle system:

    (1/a) Sin[(n*Pi*x)/(2*a)]*Sin[(m*Pi*y)/(2*a)]*Exp[-I*w*t]

    Then, I went ahead and found the complex conjugate and multiplied it by the original wavefunction. I tried to integrate it on mathematica from -Infinity to Infinity, but it said the integral does not converge.
  2. jcsd
  3. Dec 10, 2008 #2

    I belive that you are using the wavefuction for a particle in a box of length 2a. Hence, you don't have to integrate over all space - only in the box (i.e. from -a to a).

    Having a plane wave in unbound space is unphysical and not normalisable - since that would imply that the particle exists everywhere for all time.
    Last edited: Dec 11, 2008
  4. Dec 10, 2008 #3
    Right. I was working it out and that's the problem I ran into. So, if that's not how it's done, how would I go about solving this problem then?
  5. Dec 11, 2008 #4


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    Homework Helper

    Actually, this problem is quite trivial if you know that wavefunction. You don't actually have to do the integral, because you can factorize e^iwt out.
  6. Dec 11, 2008 #5
    Did you read my post? You have to integrate between "a" and "-a", and NOT from infinity to -infinity.
    Last edited: Dec 11, 2008
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