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As I understand it Blochs theorem says that the solutions to the one electron Schrödinger equation in a periodic potential has the form:
ψ(r) = exp(i k⋅r)u_{n}(r)
, where u_{n}(r) has the same periodicity as the lattice and n labels the band number.
Now a detail that confuses me: In a book I am reading (see attached picture) the function u is labeled by two quantum numbers: The band index as well as the wavenumber k. Why does u depend on the wavenumber? Am I making a fuzz out of an unimportant detail?
ψ(r) = exp(i k⋅r)u_{n}(r)
, where u_{n}(r) has the same periodicity as the lattice and n labels the band number.
Now a detail that confuses me: In a book I am reading (see attached picture) the function u is labeled by two quantum numbers: The band index as well as the wavenumber k. Why does u depend on the wavenumber? Am I making a fuzz out of an unimportant detail?
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