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Integration using exponentials 2

  1. Oct 17, 2012 #1
    1. The problem statement, all variables and given/known data


    Screenshot2012-10-17at24825AM.png

    For this forum they use the following integration:

    Screenshot2012-10-17at24832AM.png



    3. The attempt at a solution

    Where does (u+a) come from? In step 2 why does the side on the left of the plus sign become zero? In step 3, how does A(0+a√π/λ) = a

    This website likes you to work on problems but I can't work on something for which step 1 is a mystery.
     
  2. jcsd
  3. Oct 17, 2012 #2
    They do a change of variables, x-a = u, so x= u+a

    The easiest way to see this is to notice that the integrand is an odd function (that is, f(-x) = -f(x)) and therefore the integral over an even interval [-n,n] is zero.

    Did they calculate the value for A before? What you are doing here is calculating an expectation value of a random variable, so it should be true that
    [tex] \int_{-\infty}^\infty dx Ae^{-\lambda(x-a)^2} dx = 1 [/tex]

    Yes but you can't explain every single operation you do. It just seems to me you're trying to do assignments which are a bit too difficult for you. Maybe start from something easier?
     
  4. Oct 17, 2012 #3
    Thanks for your answers.

    Let's say my motivation to learn math and science right now (I'm into the humanities) on a scale of 1 to 10 is about 3. I don't have the motivation to go back and learn more calculus. I just want to see how much QM I can get through with the calc I have. Then after about 2 years hopefully I'll be able to make another effort to learn math and physics with a huge burst of motivation. This time around I dedicated about 1000 hours towards math and physics, after a two year break I'll put forth another 1000 hour effort if I have the time.
     
  5. Oct 17, 2012 #4
    But it does not speed things up if you jump over things you haven't learned/have forgotten/whatever. In fact it's likely it's making your learning slower.
     
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