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When calculating density of states for an electron, some arrive that k (the wavenumber) is $2\pi n x /L $ and some say it is $\pi n x /L$?

Where L is the dimension of the well

I’ve heard vague explanations of “you’re using only one quadrant of k space” but I truly have no idea what they’re talking about.

What is the difference in these two results and why does it occur?

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marked as duplicate by knzhou, Norbert Schuch, John Rennie, Jon Custer, tpg2114 May 13 at 23:53

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  • $\begingroup$ This might be easier to answer with the context of what is in the (parentheses). $\endgroup$ – jacob1729 May 12 at 22:29
  • $\begingroup$ Hopefully it’s clearer now $\endgroup$ – Jake Rose May 12 at 22:31
  • $\begingroup$ Basically this difference is because of boundary condition. Pi case is for zero boundary (and this you’re considering standing wave, so k can only be positive) and 2pi for periodic boundary condition (where k can be negative). $\endgroup$ – FangXie May 26 at 16:35