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Integrating a wave function

  1. Mar 24, 2005 #1
    Hey. Im pretty confident i have solve this problem. I just solve the integral of the given wave function, with the given limits... However, im having a difficult time integrating it. The sqrt(2/L) can be brought outside of the integral, but what can i with the sin function?


    The wave function of an electron is
    ψ2(x) = sqrt(2/L) sin(2πx/L)
    Calculate the probability of finding the electron between x = 0 and x = L/6.

    Cheers
     
  2. jcsd
  3. Mar 24, 2005 #2

    dextercioby

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    So what is the problem...?Compute the probability density first,and then integrate the result between the 2 limits specified in the problem...

    Daniel.
     
  4. Mar 24, 2005 #3
    One-dimensional infinite square well I assume. What's wrong?

    [tex] \psi_2 (x) = \sqrt{\frac{2}{L}} \sin{\frac{2\pi x}{L}} \Longrightarrow | \psi_2(x) |^2 = \frac{2}{L}\sin^2{\frac{2\pi x}{L}}[/tex]

    integrate from [itex]0[/itex] to [itex]\frac{L}{6}[/itex]... If you don't remember the half-angle identity, here it is:

    [tex] \sin^2{x} = \frac{1}{2}(1-\cos{2x})[/tex]
     
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