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Integration seems gaussian but the answer does not match

  1. Nov 30, 2014 #1
    1. The problem statement, all variables and given/known data




    -h^2/2m (sqrt(2b/pi)) e^(-bx^2) d^2/dx^2 (e^(-bx^2)) dx from - to + infinity







    2. Relevant equations
    I tried differentiating e^(-bx^2) twice and it came up weird , I positioned the values and finally cam up with (-2b sqrt(pi/2b)........is there any other way to do it ?

    3. The attempt at a solution
    I tried with gaussian integration and my final answer is h^2b/m but it should be h^2b/2m... how am i missing the 1/2 factor?
     
  2. jcsd
  3. Nov 30, 2014 #2

    Orodruin

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    It is difficult to say where you are going wrong if you do not show us exactly what you did step by step.
     
  4. Nov 30, 2014 #3

    Ray Vickson

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    If you mean that you came up with -2b sqrt(pi/2b) for the integral--that is, that
    [tex] \int_{-\infty}^{\infty} e^{-bx^2} \frac{d^2}{dx^2} e^{-b x^2} \, dx =- 2b \sqrt{\frac{\pi}{2b}},[/tex]
    then you are off by a factor or 2: you should have ##-b \sqrt{\pi/2b}##. You need to show your work in detail.
     
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