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Electron wave function and Probability

  1. May 21, 2012 #1
    1. The problem statement, all variables and given/known data

    I've been asked to find the value of c and the probability that the electron is located in the range of x=-1 and x=1.

    2. Relevant equations

    See Graph below

    3. The attempt at a solution

    ψ graph http://img850.imageshack.us/img850/61/wavefunction.jpg [Broken]

    |ψ|[itex]^{2}[/itex] graph http://img35.imageshack.us/img35/6663/psisquare.png [Broken]
    As mentioned by ehild the graph is not drawn with correct scale (my carelessness, which caused all my problems)

    For part a) I need to find value of C. Which I have found to be 0.577 but the answer seems wrong, I have done this by drawing a |ψ|[itex]^{2}[/itex] graph (which is almost the same except there are no negative y values. I have found c by making the area underneath |ψ|[itex]^{2}[/itex] equal to 1. Since the two smaller square in -1to -2 and 1 to 2 are exactly half I tried to find c by making the graph a rectangle with L=3nm given area must equal 1, width must equal [itex]\frac{1}{3}[/itex]. Hence I got a value for c which is [itex]\sqrt{\frac{1}{3}}[/itex] = 0.577



    For part b I am asked to fin probability of electron being in x=-1 and x=1 nm. My answer was 0.666 (0.7 as I have been asked to answer in one significant figure) but this seems wrong too.

    Anyone able to tell me where I have made mistake?

    Thanks
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. May 21, 2012 #2

    ehild

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    Homework Helper
    Gold Member

    .... and the height of the middle part is 4 times the height of the small rectangles. So you have got two rectangles of width 1 and height c2/4 and a big rectangle of width 2 and height c2.
    What is the area?


    ehild
     
  4. May 21, 2012 #3

    Thanks.

    Edit: Obviously I need to work a bit more on wave functions and finding the heights, anyone know where I could get some examples? I tried google, but it comes up with complex stuff.
     
    Last edited: May 21, 2012
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