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Physics
Atomic and Condensed Matter
Bloch momentum-space wave functions
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[QUOTE="dRic2, post: 6567551, member: 638830"] To add new states you need to add another unit cell to your array of cells. But if you add another unit cell the symmetry of the hamiltonian doesn't change at all (it's still made of a set of cells, no continuous translational symmetry), hence momentum is still not a good variable to work with. You can add how many cells you want (meaning that you are working with a finer and finer [I]k-mesh[/I]) but nothing can change. If you really want a connection with the momentum you can show (check for yourself) that the velocity operator ## \mathbf{ \hat v} ## (defined as ## \mathbf {\hat v} = \frac {-i} {\hbar} [\mathbf{\hat r}, \hat H]##) is given by (in reciprocal space): $$\mathbf{ \hat v_{\mathbf k}} = \frac 1 {\hbar } \nabla_{\mathbf k} \hat H_{\mathbf k}$$ That's as far as you can go, I guess. [/QUOTE]
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Atomic and Condensed Matter
Bloch momentum-space wave functions
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