In basic chemistry, we "fill up" the energy levels of an atom by putting two electrons in each energy level. The justification for this (that I've seen) is that the Pauli exclusion principle only allows one electron per state and there are two states in each energy level (spin up and spin down). My question is, why can't we use superposition states? My understanding is that the Pauli exclusion principle says that two fermions can't occupy the same state, but it does not require that those states be orthogonal.(adsbygoogle = window.adsbygoogle || []).push({});

As a simplified example, let's ignore spin and say that we have eigenstates of the Hamiltonian ## \left| 1 \right\rangle, \left|2\right\rangle, \left|3\right\rangle, \ldots ##. Let's say we have one electron in state ## \left| 1 \right\rangle ##. Could we then have a second electron in state ## 2^{-1/2} \big( \left|1\right\rangle + \left|2\right\rangle \big) ##? It seems to me that there is no violation of Pauli exclusion here, yet this is a lower energy configuration than having one particle in ## \left| 1 \right\rangle ## and one in ## \left| 2 \right\rangle ## (which is what we seem to usually assume).

Am I making any mistakes in my thinking here? If not, then I guess my question is why do we seem to always assume that electrons occupy eigenstates of the Hamiltonian? Why do we expect that particles should be in states of definite energy?

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# Pauli exclusion and superposition states

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