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QFT25

- 25

- 3

## Homework Statement

Using contour methods, evaluate the following integrals. In any case in which you wish to argue that some portion of a closed contour gives a negligible contribution, you should explain why that is so.

Integral[E^I(k+delta*I)x^2 dx from negative Infinity to Infinity]

as Delta tends toward positive zero.

## Homework Equations

Residue theorem which states that the the Integral of a complex function over a closed contour equals 2*Pi*I times the sum of all of it's residues which are determined by singular points.

## The Attempt at a Solution

I can't find any singularities in the integrand so I initially thought I can still use a semi circular contour and set the integral over that contour to zero. That way the integral over the real line would equal negative integral of the semi circle. But when I do that I get an exponential to the exponential which I cannot integrate. That leads me to think that my approach is wrong. I never saw an integral like this before so I'm sort of at a lost where to start. Any help will be appreciated. Note this is for a Mathematical Physics class, not a proof based complex analysis class. [/B]