Question

Write down energy dependency of density of state for photon in 1 d

Answer 1

Solution

For photon dispersion relation is given by

E=Ak

k is wave vector it's power s=1.

Then relation between energy and density of state is given by

$D(E) \propto E^{\frac{d}{s}-1}$

Here for photon

s=1 d=1

$D(E) \propto E^{\frac{1}{1}-1}$

$D(E) \propto E^0$

Means density of state is independent of energy.