It means that the number of electronic states per unit energy interval increases with the square root of the energy. There is continuous variation of energy which suggests bands have continuous allowed energy states. Is there any further significance to it?
Jürgen Weippert
Well, the DOS goes into many other calculations, so for every system that is approximately described by the 3D quasi-free electron gas from which this relation is derived you can put in this analytical expression into the equation.
In systems for which the 3D quasi-free electron gas is not fitting (e.g. everything that's not metallic) you would have to get a numerical DOS and thus integrate the follow-up equations numerically as well.
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