[UPSC CSE 2025] Schrodinger’s Wave equation and applications (Q110, 20M)

What is the density of states? For a relativistic particle of rest mass \mu, prove that the density of states in the extreme relativistic limit (E \gg \mu c^2) g(E) = \frac{V}{\pi^2 \hbar^3 c^3} E^2 where g(E) = density of states, V = volume of the system containing the particle, E = total energy, c = velocity of light and \hbar = Planck's constant.