Question

for relativistic particles, the single particle density of states was given by
g(E) =(g_sV E/ 2π^2h^3 c^3)   E ≥ mc^2. For an ideal gas of relativistic fermions at zero temperature, show that the Fermi energy is

sqrt[(E) - m44

E_F = (Usually the zero point energy is not important, and so people often subtract it off, quoting the result above minus mc^2. For instance, this is what you need to do to match with the non-relativistic result.) At very high densities, the second term under the square root dominates over the first term. Write the first two terms in a series expansion of E_F in this limit (i.e. write the leading term and the first subleading term in the limit of large N/V ).