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Commit a10c8fd4 authored by Lars kleyn Winkel's avatar Lars kleyn Winkel
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Update 8_many_atoms.md

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...@@ -206,7 +206,7 @@ The spacing of the distorted chain alternates between two different distances an ...@@ -206,7 +206,7 @@ The spacing of the distorted chain alternates between two different distances an
![](figures/peierls_transition.svg) ![](figures/peierls_transition.svg)
Due to the alternating hopping energies, we must treat two consecutive atoms as two different orbitals ($\left| n,1 \right>$ and $\left| n,2 \right>$ in the figure) from the same unit cell. The corresponding LCAO of this chain is given by $$\left|\Psi \right> = \sum_n \left( \phi_n \left| n,1 \right> + \psi_n \left| n,2 \right>\right).$$ As usual, we assume that all these atomic orbitals are orthogonal to each other. Due to the alternating hopping energies, we must treat two consecutive atoms as two different orbitals ($\left| n,1 \right>$ and $\left| n,2 \right>$ in the figure) from the same unit cell. The corresponding LCAO of this chain is given by $$\left|\Psi \right> = \sum_n \left( \phi_n \left| n,1 \right> + \psi_n \left| n,2 \right>\right)$$ As usual, we assume that all these atomic orbitals are orthogonal to each other.
1. Indicate the length of the unit cell $a$ in the figure. 1. Indicate the length of the unit cell $a$ in the figure.
2. Using the Schrödinger equation, write the equations of motion of the electrons. 2. Using the Schrödinger equation, write the equations of motion of the electrons.
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