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Math Help - Normalising A given Gauss Integral with a constant coefficient

  1. #1
    Senior Member bugatti79's Avatar
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    Normalising A given Gauss Integral with a constant coefficient

    Dear Folks,

    I need to normalise a wave function by solving for A given that

    1=A^2 \int^{\infty}_{-\infty} e^{-\frac{m\omega x^2}{\hbar}}dx

    The gauss integral is given as
     \sqrt {\pi}=\int^{\infty}_{-\infty} e^{-x^2}dx

    How do I handle the constant (mw/h)? I tried substitution but it broke down...

    Thanks
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  2. #2
    Flow Master
    mr fantastic's Avatar
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    Quote Originally Posted by bugatti79 View Post
    Dear Folks,

    I need to normalise a wave function by solving for A given that

    1=A^2 \int^{\infty}_{-\infty} e^{-\frac{m\omega x^2}{\hbar}}dx

    The gauss integral is given as
     \sqrt {\pi}=\int^{\infty}_{-\infty} e^{-x^2}dx

    How do I handle the constant (mw/h)? I tried substitution but it broke down...

    Thanks
    Substitute \displaystyle u = \sqrt{\frac{m \omega}{\hbar}}x. If you need more help, please show all your work and say where you get stuck.
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  3. #3
    Senior Member bugatti79's Avatar
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    Quote Originally Posted by mr fantastic View Post
    Substitute \displaystyle u = \sqrt{\frac{m \omega}{\hbar}}x. If you need more help, please show all your work and say where you get stuck.
    Thanks Mr Fantastic,
    See attached jpg.
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  4. #4
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    Quote Originally Posted by bugatti79 View Post
    Thanks Mr Fantastic,
    See attached jpg.
    Sorry, but the last lines that begin with "I attempted" are completely wrong. If you are trying to derive the general result, I suggest you Google:

    integral gaussian

    or similar search string to find the correct approach.
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  5. #5
    Senior Member bugatti79's Avatar
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    I know it was completely wrong...thats what I wrote on the last line, my attempt was 'rubbish'. Sorry for bad writing!!!

    I was aware of the gauss integral but I didnt know how to perform the correct substitution

    Cheers
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