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I am having trouble with the meaning of the $k$ vectors in an energy diagram. If I want to populate some band, let say using a laser, what will be the significance of $k$? Does it correspond to the polarization angle with respect to particular planes?

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It refers to the wave vector. See the Wikipedia article on band structure or these lecture notes for some explanations. If something is still unclear after going through the basics, feel free to ask another question.

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Thanks. It is quite abstract as thinking of wave vector. I wanted to understand how can I populate a specific band at some k location with light. And what is the meaning of k=0 these states are not allowed for particle in a box because of the uncertainty principle .. –  Anonymous Sep 9 '13 at 4:41
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