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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?


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