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Normalization of wave function (Griffiths QM, 2.5)

  1. Nov 30, 2012 #1
    1. The problem statement, all variables and given/known data
    A particle in the infinite square well has its initial wave function an even mixture of the first two stationary states:

    [itex]\Psi(x,0) = A\left[ \psi_1(x) + \psi_2(x) \right] [/itex]

    Normalize [itex]\Psi(x,0)[/itex]. Exploit the orthonormality of [itex]\psi_1[/itex] and [itex]\psi_2[/itex]



    2. Relevant equations
    [itex]\psi_n(x) = \sqrt{\frac{2}{a}} \sin \left( \frac{n\pi}{a}x\right)[/itex],
    where a is the width of the infinite square well.


    3. The attempt at a solution
    I've managed to eliminate the orthogonal parts of my integral, so I'm now left with
    [itex]|A|^2 \int |\psi_1|^2 + |\psi_2|^2 dx = 1[/itex]

    I have the feeling that I now have to exploit the fact that they are both normalized, but why is that so? What's the logic here?

    EDIT: I had written a wrong expression for [itex]\psi_n[/itex]. Sorry! :(
     
    Last edited: Nov 30, 2012
  2. jcsd
  3. Nov 30, 2012 #2
    Solution: The expression for [itex]\psi_n[/itex] is already normalized. I should have realized this. Therefore, the integral yields 2 over the interval
     
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