I was looking at the derivation for density of states for particle in 3D box potential and 3D harmonic potential. In the case of box potential, there is a volume term where as in the case of harmonic there is no such terms for volume (Please find the image below for the expression of density of states). But from definition of density of states, we consider a number of state between energy dE or volume of phase smaller than E to volume occupied by single quantum state. So, Is the volume element hiding in the later case or what is the volume for a harmonic potential ? Any comments are appreciated. enter image description here

  • $\begingroup$ Would you state the source of the excerpt/picture :)? Thanks! $\endgroup$
    – Cheng
    Dec 21, 2022 at 14:03


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