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Energy Band in a solid

  1. Feb 21, 2013 #1
    n is the band index and k is the electron wave vector. Now is energy band specified when for each n , k runs through all the values available that specify periodic boundary conditions ?

    But in Ashcroft Mermin , it is also given that for a given k , there exists an infinite family of solutions labelled by n which is the band index.

    I am confused here about what specifies the band.
     
  2. jcsd
  3. Feb 21, 2013 #2

    DrDu

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    Look at it like this: k determines the boundary conditions for an elementary cell, namely the value of the logarithmic derivative of the wavefunktion ##\psi'/\psi (a)=\psi'/\psi(0) \exp(ika)##.
    Now the Schroedinger equation in a single cell, with the boundary condition specified by k, has an infinity of solutions labelled by n.
     
  4. Feb 21, 2013 #3
    So the second one is correct ans.
     
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