Gaussian Integral

  • Thread starter smallgirl
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  • #1
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Hey,

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]

[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...
 

Answers and Replies

  • #2
mathman
Science Advisor
7,877
453
Hey,

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]

[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...
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:

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