Timeline for Second quantization: periodicity of annihilation and creation operators in momentum space, originally on a lattice
Current License: CC BY-SA 4.0
3 events
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| May 27, 2020 at 7:43 | comment | added | user245141 | at least for uniform hopping you're not supposed to get that... I see that you have periodicity $\beta$, which means that you need to define a unit cell and take the FT with respect to that (Bloch theorem) | |
| May 26, 2020 at 8:40 | comment | added | Feynman's Cat | If I follow your definition of the annihilation operator $a_n$ in terms of $a_k$ (which I understand and I realize why my question is erroneous in that part) and substitute it in $H$, say I get terms like $\int dk \int dk' f(k,k') \, \delta(k-k'+\pi)$, where $k,k'$ are momenta. What would happen to this integral? I should naively get $f(k,k+\pi)$ but $k+\pi$ could lie outside the Brillouin zone. Also, since $k$ is periodic by $2\pi$, should $a_{k+\pi} = a_{k-\pi}$? I am concerned about the periodicity of $a_k$ mainly. | |
| May 26, 2020 at 8:19 | history | answered | user245141 | CC BY-SA 4.0 |