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Homework Help: Bloch theorem

  1. Jan 14, 2009 #1
    This is not any homework problem but just something I don't understand. The Bloch theorem states that
    [tex]\psi(\textbf{r}+\textbf{R})=e^{i\textbf{k}\cdot \textbf{R}}\psi(\textbf{r})[/tex]

    Now the k is a vector in the reciprocal lattice (usually in the first Brillouin zone), which is defined as the set of vectors K that satisfy
    [tex]e^{i\textbf{K}\cdot\textbf{R}}=1[/tex]

    Now, if k points to a point in the reciprocal lattice, then why isn't the Bloch theorem
    [tex]\psi(\textbf{r}+\textbf{R})=e^{i\textbf{k}\cdot \textbf{R}}\psi(\textbf{r})[/tex]
    just
    [tex]\psi(\textbf{r}+\textbf{R})=1\psi(\textbf{r})[/tex]?
     
  2. jcsd
  3. Jan 15, 2009 #2

    turin

    User Avatar
    Homework Helper

    AFAIK, k is not limited to a reciprocal lattice vector. I think that would only be for standing waves. The complex phase gives the wave a direction.
     
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