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Normalizing the function

  1. Nov 7, 2014 #1
    1. The problem statement, all variables and given/known data
    I have to normalize the function below:
    Y(k)= A (a-|k|) where |k|<=a ; And Y(k)=0 where |k|>a

    2. Relevant equations


    3. The attempt at a solution

    I just get to infinity.
     
  2. jcsd
  3. Nov 7, 2014 #2

    Simon Bridge

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    ... how?
    ... sketch Y vs k for the function.
    What shape is it? What is the equation for the area of that shape?
     
  4. Nov 7, 2014 #3
    I know how does it shape but I still don't understand how does the integral of Y^2 should be solved.
     
  5. Nov 7, 2014 #4

    Simon Bridge

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    ... so what is the shape? If you don't answer questions it is difficult to help you.

    Show me what you are trying.
    Unless I see how you are thinking I don't know how to help you.
     
    Last edited: Nov 7, 2014
  6. Nov 7, 2014 #5
    First one is what I got in normalizing. I can't solve the last two integrals while the fist one is infinity.
    And below is what I guess the shape of the function Y(k) should be.
    image.jpg
     
  7. Nov 7, 2014 #6

    Simon Bridge

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    OK, you are starting out with: ##Y(k)=A(a-|k|) : |k|<a, 0 \text{ otherwise}##

    To normalize ##Y##, you need to find ##A: \int_{-\infty}^\infty Y^\star Y\;dk = 1## Since Y is real, ##Y^\star Y = Y^2##

    In your attachment I only see you taking the range from a to +infinity.
    But the wavefunction is defined over all values of k.

    Note: you are mistaken about what shape the wavefunction is;
    ... what is the value of Y when k > a? What did you put on your sketch?
     
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