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Atomic and Condensed Matter
Don't understand proof of Bloch theorem
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[QUOTE="Twigg, post: 6405612, member: 572426"] I'm no crystallographer, but my guess is that they made a knock-off "dot product" to shorten the notation and look like a cool kid. There's a "dot product" like this for the Pauli matrices too. In a crystal with low symmetry, a1,a2,a3 need not be orthogonal (like in a triclinic? I'm not sure on the nomenclature don't quote me), so really this "dot product" is pure notation. Like with the Pauli matrix "dot product", ##\vec{a}## here is just a "vector" whose "elements" are the vectors ##\vec{a_1}##,##\vec{a_2}##,##\vec{a_3}##. ##\vec{n}## is just a vector of integers here. [/QUOTE]
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Atomic and Condensed Matter
Don't understand proof of Bloch theorem
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