Hey everyone,(adsbygoogle = window.adsbygoogle || []).push({});

I'm having some trouble understanding this, any help would be appreciated:

Calculate the density of states for a free particle with momentum [tex]\[

\hbar k

\]

[/tex] for the angles between [tex]\[

\left[ {\theta _0 ,\theta _0 + d\theta } \right]

\]

[/tex] relative to an electric field [tex]\[

\vec \varepsilon

\]

[/tex], in the ultra-relative limit [tex]\[

E \cong pc

\]

[/tex].

In my solutions, the first thing they do is to say: Well, as usual, first find [tex]\[

N\left( E \right)

\]

[/tex] and then take the derivative with respect to [tex]\[

E

\]

[/tex], but that's OK. The problem is how they calculate [tex]\[

N\left( E \right)

\]

[/tex]:

[tex]\[

N\left( E \right) = \frac{V}{{h^3 }}\int\limits_{\theta \in \left[ {\theta _0 ,\theta _0 + d\theta } \right]} {d^3 p} = \frac{V}{{h^3 }}2\pi \sin \left( {\theta _0 } \right)d\theta \int\limits_0^{p_{\max } } {p^2 d^2 p}

\]

[/tex]

I can live with the first move. But I don't understand where this sine comes from, or [tex]\[

2\pi

\]

[/tex], and that other integral... help?

Thanks in advance!

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

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!

# Weird state density calculation

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