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What happens at energy-gaps, Kronig-Penney model

  1. Apr 11, 2015 #1
    I'm studying periodic boundaries in 1D for which energy gaps occur, i.e. values of the energy which are not allowed, according to the Kronig-Penney model. My question is when these band gaps occur what happens to the wave-function, because it still has to be continuous, so it can't just terminate, so does it stay the same? Or what happens to the wave-function at these regions?

    Thanks!
     
  2. jcsd
  3. Apr 16, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
  4. Apr 17, 2015 #3

    DrDu

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    The wavefunctions don't have to be continuous as a function of E, the spectra of atoms or molecules serve as a counter example. For free electrons, the wavefunctions are somehow continuous as a function of k and E, but, there are always two degenerate solutions with the same value of E, namely those with k and -k. The periodic potential will lift this degeneracy, i.e. while for a free particle the functions exp ikx and exp -ikx, or equivalently, cos kx and sin kx are degenerate, with a weak potential, the functions cos kx and sin kx are eigenfunctions belonging to different energies.
     
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