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Gaussian Integral

  1. Jan 28, 2014 #1

    I am rather stuck on this gaussian integral....

    I have come this far, and not sure what to do now:

    [tex]\int dh_{01}(\frac{h_{01}}{\sigma})^{2}+\frac{\Delta k^{2}(t-x)^{2}h_{01}}{2}-ik_{0}(t-x)h_{01}[\tex]

    [tex]\int dh_{01}(\frac{h_{01}}{\sigma})^{2}+k_{0}(t-x)h_{01}(-i+\frac{\Delta k^{2}(t-x)}{2k_{0}})

    [tex]\int dh_{01}(-((\frac{h_{01}}{\sigma}-\frac{\sigma}{2}k_{0}(t-x)\int dh_{01}(\frac{h_{01}}{\sigma})^{2}+k_{0}(t-x)h_{01}(-i+\frac{\Delta k^{2}(t-x)}{2k_{0}}))[\tex]

    [tex]\int dh_{01}(\frac{h_{01}}{\sigma})^{2}+k_{0}(t-x)h_{01}(-i+\frac{\Delta k^{2}(t-x)}{2k_{0}}))^{2})-\frac{\sigma^{2}}{4}(t-x)^{2}k_{0}^{2}(-i+\frac{\Delta k^{2}(t-x)}{2k_{0}})^{2}[\tex]

    where a=-1 b=1/2

    Not sure what to do now...
  2. jcsd
  3. Jan 28, 2014 #2


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    Science Advisor

    You need to change \tex to /tex. Even so, the equations look wierd. It is not at all clear what you are doing.
    Last edited: Jan 28, 2014
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