- #1
Petar Mali
- 290
- 0
In solid state we often have case
[tex]\sum_{\vec{k}}F(\vec{k})=\frac{V}{h^3}\int_{I bz} F(\vec{p})d^3\vec{p}[/tex]
Integral goes into first Briolen zone.
We can always say that
[tex]\frac{V}{h^3}\int_{I bz} F(\vec{p})d^3\vec{p}=4\pi \frac{V}{h^3}\int^{\infty}_{0}F(p)p^2dp[/tex]
In 2D we will have integral
[tex]\frac{S}{h^2}\int_{I bz} F(\vec{p})d^2\vec{p}[/tex]
where [tex]d^2\vec{p}=2\pi pdp[/tex]
Am I right?
Can you tell me what I will have in 1D? Thanks!
[tex]\sum_{\vec{k}}F(\vec{k})=\frac{V}{h^3}\int_{I bz} F(\vec{p})d^3\vec{p}[/tex]
Integral goes into first Briolen zone.
We can always say that
[tex]\frac{V}{h^3}\int_{I bz} F(\vec{p})d^3\vec{p}=4\pi \frac{V}{h^3}\int^{\infty}_{0}F(p)p^2dp[/tex]
In 2D we will have integral
[tex]\frac{S}{h^2}\int_{I bz} F(\vec{p})d^2\vec{p}[/tex]
where [tex]d^2\vec{p}=2\pi pdp[/tex]
Am I right?
Can you tell me what I will have in 1D? Thanks!