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Homework Help: Wave funtion and normalisation constant

  1. Apr 27, 2010 #1
    1. The problem statement, all variables and given/known data
    find the normalisation constant (A)



    2. Relevant equations
    wave functcion
    [tex] \psi (x,t)= A[3sin(\frac{\pi x}{L})+2sin(\frac{2\pi x}{L}][/tex]


    3. The attempt at a solution
    [tex] A^2\int_{0}^{L}[\psi(x,t)]^2dx=1[/tex]
    [tex] A^2\int_{0}^{L}[9sin^2(\frac{\pi x}{L})+12sin(\frac{\pi x}{L})sin(\frac{2\pi x}{L})+4sin^2(\frac{2\pi x}{L})}]dx[/tex]
    1. The problem statement, all variables and given/known data

    i try to solve each integral separately
    I have started with the first one and i got

    [tex] A^2\int_{0}^{L}[9sin^2(\frac{\pi x}{L})]dx= A^2\cdot \frac{9L}{ \pi}\int_{0}^{\pi}sin^2tdt=A^2\cdot \frac{9L}{\pi}[\frac{1}{2}t+\frac{sin(2t)}{4}]\right]_{0}^{\pi}=A^2\cdot \frac{9}{2}L[/tex]
    is it correct so far?

    from the last integral i got
    [tex]A^2\frac{L}{\2\pi}\int_{0}^{2\pi}4sin^2(2t)dt=A^22L[/tex]

    i dont have a good idea for solving the second intregral....
     
    Last edited: Apr 27, 2010
  2. jcsd
  3. Apr 27, 2010 #2
    use the fact that, 2 sin A sin B = - cos (A + B) + cos (A - B) ..
     
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