Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Density of states

  1. May 12, 2012 #1
    Consider waves in a box. It is customary to calculate the density of states either by enforcing vanishing boundary conditions, then the wave numbers are
    [itex]k=\frac{n\pi}{L}[/itex] and we take only positive [itex]k[/itex],
    or using periodic boundary conditions, in which case [itex]k=\frac{2n\pi}{L}[/itex]
    and taking all wave numbers.

    My question is - why in the case of vanishing boundary conditions do we take only positive wave numbers? and why in the case of periodic boundary conditions do we take both positive and negative?
  2. jcsd
  3. May 14, 2012 #2


    User Avatar
    Science Advisor

    In the first case, vanishing boundary conditions, the solutions are standing waves, and the solutions for +k and -k are exactly the same. So we use just positive k to avoid counting them twice.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook