Gaussian Integral

1. Jan 28, 2014

smallgirl

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...

2. Jan 28, 2014

mathman

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