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Problem with Integration

  1. Jan 11, 2005 #1
    I've recently posted a thread asking for help in the Homework forum in solving this problem, but till now I still can't figure out how do find the solution to this equation.

    Here is the problem.

    Show that [tex]A=(\frac{m\omega}{\hbar\pi})^{1/4}.[/tex]

    From the normalisation condition

    [tex]|A|^2\int_{-\infty}^{\infty} e^{-2ax^{2}}=1[/tex]

    Where [tex]a =\frac{\sqrt{km}}{2\hbar}[/tex]

    I'm really have no idea on how do solve this problem. Does this solving this problem require the use of Fourier Transform?
     
  2. jcsd
  3. Jan 11, 2005 #2

    dextercioby

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    No,just the Poisson integral:
    [tex] I_{1}(a)=:\int_{-\infty}^{+\infty} e^{-ax^{2}} dx =\sqrt{\frac{\pi}{a}} [/tex]

    Daniel.

    PS.In physics,this integral is widely used...
     
  4. Jan 11, 2005 #3
    Ohhhhh...

    Never heard of it :grumpy: That made things whole a lot simpler.
     
  5. Jan 11, 2005 #4

    dextercioby

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    Then how the heck were u supposed to do that integral??I'm sure it's about HLO in QM...You should know a lotta calculus for QM...

    Daniel.
     
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