1. The problem statement, all variables and given/known data Find the density of states g(ε) for an ideal quantum gas of spinless particles in dimension d with dispersion relation ε= α|p|s , where ε is the energy and p is the momentum of a particle. The gas is conﬁned to a large box of side L (so V = Ld) with periodic boundary conditions. The density of states is deﬁned as the number of single particle energy states with energy between ε and ε + dε. You can use the volume of a d-dimensional sphere of radius R, Ω0 = 2πd/2/dΓ(d/2)Rd. 3. The attempt at a solution In 3D we solved this problem by solving the Schrodinger eq. where ε~p2 but what happen when the dispersion relation is ε= α|p|s? My attempt was to define Γ(ε) as the number of states with energy ≤ ε in d- dimentions Γ(ε) = the volume of a d-dimensional sphere of radius n(ε) (n ia the quantum num) g(ε)=dΓ(ε)/dε but how can i find the relation between n and ε? is it ok to say : p=(h/2π)k and k=πn/L and then just put it in the dispertion relation? Thank you!