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!

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

    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) ..
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Wave funtion normalisation Date
Proving a complex wave satisfies Helmholtz equation Monday at 12:33 AM
Step potential, continuous wave function proof Feb 19, 2018
Recurrence relation for harmonic oscillator wave functions Nov 18, 2017
Wave funtions Mar 5, 2006