Greetings! It is easy to understand that for a free electron, we can easily define the energy state density, and by doing the integration of the State density* Fermi-Dirac distribution we will be able to figure out the chemical potential at zero kelvin, which is the Fermi-Energy. Hence, we can define the Fermi Momentum correspondingly. However, I feel rather struggling to define the fermi-momentum and Fermi energy for a non-parabolic dispersion. Say, For example, A 2D system, I have a dispersion E = A*k^2 +B*k^3 So k(E) will be in general complicated due to its cubic relations. So If we still want to evaluate the Fermi Energy, Do still solve the integration int _0 ^E_f state density*Fermi-Dirac Distribution dE = Number of Particles to evaluate E_f? And I think this integration will be very complicated. Also, Under this circumstance, how do we define the Ferim-Momentum? Do we still solve E_f = A k_F^2 + B k_F^3 to find k_F? Thanks!