The density of states related to volume V and N countable energy levels is defined as: D ( E ) = 1 V ∑ ∑ i = 1 N δ δ ( E − − E ( k i ) ) . Because the smallest allowed change of momentum k for a particle in a box of dimension d and length L is ( Δ Δ k ) d = ( 2 π π / L ) d , the volume-related density of states for continuous energy levels is obtained in the limit L → → ∞ ∞ as D ( E ) := ∫ ∫ R d d d k ( 2 π π ) d ⋅ ⋅ δ δ ( E − − E ( k ) ) , Here, d is the spatial dimension of the considered system and k the wave vector.