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Questions on the defination of wave number and propagation constant in energy gaps

  1. Sep 3, 2006 #1
    Hi, I just get confused on the some definations in the energy gap theory.

    in the equation
    [tex]
    \cos {k_1a} \cos{k_2b} - \frac{k_1^2 + k_2^2}{2k_1k_2} \sin {k_1a} \sin{k_2b} = \cos {kd}
    [/tex]
    where
    [tex]
    \frac {\hbar ^2 k_1^2}{2m} = E
    [/tex]
    [tex]
    \frac {\hbar ^2 k_2^2}{2m} = E - V
    [/tex]

    however the eigenergies
    [tex]
    \frac {\hbar ^2 k^2}{2m} = E
    [/tex]

    Here I just get confused
    what is the physical meaning of k1,k2 and k?
    and what is the difference of the energy calculated from k and k_1?
     
    Last edited: Sep 3, 2006
  2. jcsd
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