# Fourier transforms

1. Apr 19, 2010

### scigal89

My teacher worked out the following and said it's a unitary transformation (how?) of exp(ikx). He said we're supposed to find the periodic bounds of integration - but I thought for Fourier transforms the bounds are negative infinity to infinity, so in this case shouldn't it just be the Dirac delta function? Also, how do you get the 2 in front of the sin? When I rewrite using Euler's identity, there is no 2.

$$\int e^{ik(x-x')}dk=\frac{e^{ik(x-x')}}{i(x-x')}\approx \frac{2sin[k(x-x')]}{x-x'}$$

He then substituted x' with the deBroglie wave length at the Fermi level. I'm not sure what the physical meaning is...

Last edited: Apr 19, 2010