1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook