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Plants harvest light with near perfect efficiency, but this is impossible under classical physics. Along the way to the photosynthzing core, photons should collide with other particles, but they don't. A photon reaching the core is as likely to succeed as you sprinting through a dense forest blindfolded trying to get to the center of the forest without ...


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I am not sure about the equation in your question - it looks too simple to me. I think there should be separate $\phi$ functions for $2s$ and $2p_{x,y,z}$ on each of the 6 carbon atoms as well as the $1s$ on the hydrogen. I am more used to LCAO (linear combination of atomic orbitals) than tight binding, but apparently these two methods are quite similar. ...


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The reason is that also other orbitals are occupied. For example for benzene using the hückel-method you will find following molecular orbitals. The three lowest lying are occupied because of the 6 electrons. The pauli exclusion principle cannot be violated!


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Well, you might not really want to overthink it. It all hinges on the Pauli matrix $\sigma_1$ which, yes, is the permutation group with two components, with eigenvalues $\pm 1$ for $v^T=(1,1)$, symmetric, and $w^T=(1,-1)$, antisymmetric, respectively. Equivalently to your decomposition, you may write the hamiltonian as $$ H= \epsilon_0 I_4 + ...



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