(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

According to the non-relativistic quantum mechanics of a particle of mass m in a cubic box ov volume V = L^{3}, the single particle energy levels are given by

E_{k}=[itex]\hbar[/itex]^{2}k^{2}/2m

where k is the magnitude of the wavevector K = (kx,ky,kz) and where the components of k are quantised as kx=[itex]\pi[/itex]nx/L etc with nx=0,1,2,...

a)Show that the density in the k-space of the single particle states that are available to electrons is given by

[itex]\rho[/itex]=Vk^{2}/[itex]\pi[/itex]^{2}

2. Relevant equations

3. The attempt at a solution

In my notes I have the derivation of this, however it shows it to be 2[itex]\pi[/itex]^{2}in the denominator, as do other online sources.

Is there something I'm missing that means in this situation the factor of can be taken out?

(There are further parts to this question that ask to prove certain things that only hold true without the factor of 2 so it's not an error)

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Density of states

**Physics Forums | Science Articles, Homework Help, Discussion**