# Strange Integral Notation

• Aug 12th 2010, 07:57 PM
Mentia
Strange Integral Notation
Hi folks, I am having some trouble with an integral involving a delta function. I have been working with calculus for many years and have never seen the particular notation given in the following integral, I am quite confused by the $d^{3}k$.

$2\int \frac{d^{3}k}{(2 \pi )^{3}}\delta \left ( E-\frac{\hbar^{2}k^{2}}{2m} \right )= \frac{1}{2 \pi ^{2}}\left ( \frac{2m}{\hbar ^{2}} \right )^{3/2} \sqrt[]{E}\Theta \left ( E \right )$

Notice this is an integral over the dirac delta function and it spits out a unit step function (Theta).

Can someone please explain what it means by $d^{3}k$ and perhaps a few steps between the integral and the solution? Thanks.
• Aug 12th 2010, 08:26 PM
Vlasev
This notation is frequently used in physics. the dk just means dkdkdk so it's a triple integral. Unfortunately i don't know how to helo you with the evaluation.