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By the Pauli-Exclusion Principle, no two electrons can be in the same quantum state. So, how can both be in the same energy eigenstate?

Atom orbitals certainly have more than one electron per energy level. Is this because the electrons don't inhabit the exact same quantum state, just quantum states with the same energy eigenvalue due to degeneracy?

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Is this because the electrons don't inhabit the exact same quantum state, just quantum states with the same energy eigenvalue due to degeneracy?

Yes. An electron around a hydrogen atom has four quantum numbers: the principal quantum number $n$, the azimuthal quantum number $l$, the magnetic quantum number $m$, and the spin quantum number $s_z$. Two electrons with different values of any of these quantum numbers are in different states as far as the Pauli exclusion principle is concerned, but the energy is (to a good approximation) only dependent on $n$.

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