Density of states arbitrary units

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So the problem is following. The density of states in energy space (3D case) represents the number of states per unit volume per energy. This means that the unit is #(number of states)/(cm^3 eV). This result can be seen in many solid-state physics books.
I am reading some articles where the density of states for different layers is calculated using computer simulations and where the density of states is given in arbitrary units in energy space. What is the meaning of using the arbitrary units for DOS? Shouldn't it be in some form of number of states per unit volume (area or length) per energy? How do I convert that results to #/(cm^3 eV)
 

TeethWhitener

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What is the meaning of using the arbitrary units for DOS?
They likely were focusing on reporting qualitative features of the DOS. It is a tad annoying; I agree. But it’s pretty standard practice, especially in computational papers.

Another place where you see arbitrary units used frequently is in spectroscopy, where line intensity will generally be reported in arbitrary units unless the paper is specifically reporting absolute oscillator strength. This is because 1) line intensity depends on the intensity of the excitation source, and 2) the most salient features of most spectra (wavelength/frequency, relative intensity between lines, linewidth, etc.) are not related—or are only weakly related—to absolute intensity.
Shouldn't it be in some form of number of states per unit volume (area or length) per energy? How do I convert that results to #/(cm^3 eV)
Yes, it should, and you can’t. There’s no way to know what the units correspond to; they’re arbitrary.
 

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