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Normalization Calculation

  1. Sep 14, 2014 #1
    1. The problem statement, all variables and given/known data

    Using the normalization condition, find the constants λ and a of:

    f(t)=ae^(-λt)



    2. Relevant equations
    integrate from t=-∞ to t=∞
    of the function and set it equal to one

    3. The attempt at a solution

    I used to be good at these but something is slipping my memory...

    I used u substitution to integrate by hand and I've gotten to the step...

    a/-λ[(e-λt evaluated at ∞) - e-λt evaluated at -∞] =1


    now, I'd say the left term in the bracket is 0 because as t goes to infinity that term drops to zero, assuming a positive value of λ. so I'm left with

    a/-λ [- e-λt = 1... I'm stuck at this point because to me that term would blow up to infinity so what am I missing? thanks
     
  2. jcsd
  3. Sep 14, 2014 #2

    vela

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    The problem as you wrote it doesn't have a solution because, as you found out, the integral won't converge. Are you sure that's the problem as it was given to you? Are you sure about the integration limits?
     
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