If time evolution of a general ket is given by | Ψ > = e(adsbygoogle = window.adsbygoogle || []).push({}); ^{-iHt/ħ }| Ψ (0) > where H is the Hamiltonian. If i have a eigenbasis consisting of 2 bases |a> and |b> of a general Hermitian operator A and i write e^{-iHt/ ħ }|a> = e^{-iEat/ ħ }|a> and e^{-iHt/ħ }|b> = e^{-iEbt/ ħ }|b> ; does this mean that operator A and the Hamiltonian share a set of eigenfunctions ? ie they commute ?

And how would the time evolution of a ket be written if its operator did not commute with the Hamiltonian ?

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# I Simultaneous eigenfunctions

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