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Help with an Integral

  1. Jan 21, 2006 #1

    eep

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    Hi,
    I'm having problems integrating the following function:
    [tex]\int^\infty_{-\infty}Ae^{-\lambda(x - a)^2}[/tex]
    Where A, [itex]\lambda[/itex], and a are positive, real constants. If anyone could point me in the right direction I'd really appreciate it.

    The integral is supposed to be equal to 1 and using that fact I'm supposed to solve for A. This is from Griffiths' Quantum Mechanics Chapter 1.
     
    Last edited: Jan 21, 2006
  2. jcsd
  3. Jan 21, 2006 #2

    StatusX

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    Homework Helper

    You can do the substitution u=x-a (you shouldn't actually have to do that, just think about what it would do), and then use the fact that:

    [tex]\int_{-\infty}^{\infty} e^{-a x^2} dx = \sqrt{\frac{\pi}{a}}}[/tex]

    That's something worth memorizing, but you can derive it using the technique shown on this page.
     
    Last edited: Jan 21, 2006
  4. Jan 22, 2006 #3

    eep

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    Thank you! So assuming I made the correct substitutions and such I end up with the integral being equal to:

    [tex]A\sqrt{\frac{\pi}{\lambda}}[/tex]

    And since the integral is equal to 1 (it's a probability thing)

    [tex]A = \sqrt{\frac{\lambda}{\pi}}[/tex]
     
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