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Math Help - need help to calc. this integral

  1. #1
    rem
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    need help to calc. this integral

    integral from lim 0 to infinity of { [1/ (p^2+a^2) ] * e (-ibp) }dp

    where i=(-1)^.5

    a,b=const.

    p= momentum

    if anyone have mathematica plz.help me calc it.atleast tell how to proceed with the integral.does it fall under any std. integral.form.

    can any of you suggest any book or site from which i can figure how to solve it.
    plz. it's urgent i need to this result by monday.
    Last edited by mr fantastic; February 21st 2009 at 03:22 PM. Reason: Reduced the font size to normal and made it easier to read.
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  2. #2
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    I would like to help you but I can't figure out what you want to calculate. Can you type it in LaTeX or in a code that I can paste into Wolfram Mathematica?
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  3. #3
    Senior Member Peritus's Avatar
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    you can look at it as the Fourier transform of the following function:
    <br />
F\left\{ {\frac{1}<br />
{{p^2  + a^2 }}u(p)} \right\}\left( b \right)<br />

    where u(t) is the Heaviside step function. Using the duality principle and the following transform:

    Fourier Transform--Exponential Function -- from Wolfram MathWorld

    might help you solve this integral
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  4. #4
    rem
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    trying to evaluate density correlation fn.

    Quote Originally Posted by james_bond View Post
    I would like to help you but I can't figure out what you want to calculate. Can you type it in LaTeX or in a code that I can paste into Wolfram Mathematica?
    i'm sorry.i don't have latex.
    i'm trying to evaluate density correlation fn. for a free particle

    f(q,t)=∫1/(e(cH)+1) * e(iqx) *e-(iq[x+p/m)dpdx
    =∫∫e-(cH) * e-(iqp/m)dp dx
    where c=1/kt
    p=dx/dt
    and H=p^2/2m for a free particle.
    1/(e(cH)+1) is due fermi dirac statistics
    and ∫dx can be removed using normalisation

    hence currently i'm having trouble with the momentum term.
    after taking limits e^(cH)>>1i.e.T being very low
    it reduces to classical boltzmann statistics i was able to evaluate it.

    but for larger values of T i.e. e^(ch) comparable with 1 i'm having trouble evaluating it.
    after much manipulation i got the term as
    f(q,t)=∫1/(p^2+a^2) * e-ibp dp

    thanks for your response.
    hope this will help you understand the problem.
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