Register to reply

K space sum to integral

by aaaa202
Tags: integral, space
Share this thread:
aaaa202
#1
Mar31-14, 05:09 PM
P: 1,005
How is it exactly i convert between a k-space sum an integral?
Assume that we have some macroscopic solid. Periodic boundary conditions leads to kx,ky,kz = 2π/L, so each k-space state fills a volume (2π/L)3 or has a density of V/(2π)3. To then count for instance the number of state with wavevector k<k0, what do you then do?
Intuitively I would multiply the volume of a cube of radius k0, but how does this translate into an integral exactly?
Phys.Org News Partner Physics news on Phys.org
New complex oxides could advance memory devices
'Squid skin' metamaterials project yields vivid color display
Scientists control surface tension to manipulate liquid metals (w/ Video)
andrien
#2
Apr3-14, 08:10 AM
P: 1,020
##∑_k=\frac{V}{(2\pi)^3}∫d^3k##
DrDu
#3
Apr3-14, 02:50 PM
Sci Advisor
P: 3,633
You can also write the sum as an integral over a sum of delta functions.
For slowly varying test functions, the delta functions may then be replaced by their density ##V/(2\pi)^3##.


Register to reply

Related Discussions
Convert integral over phase space to integral over energy Classical Physics 0
Harmonic oscillator phase space integral Classical Physics 2
Path integral in momentum space Quantum Physics 0
Improper Integral in 3-Space Calculus & Beyond Homework 5
Integral in an infinte dimensional space... Calculus 1