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So, I understand that quantum systems can be in superpositions of eigenstates. Why is it that we talk about electrons in hydrogen either being in the 1s orbital, or the 2s, or the 2p, etc.? Could I have an electron that is a superposition of two orbitals, say 1s and 2s?

I know from Griffiths that an incident light wave at the transition frequency causes the electron to be in an oscillating superposition, such that one has to time the measurement just right to catch the electron in a state of high probability with respect to the higher orbital. What if I turn the sinusoidal perturbation off while the electron is still in a superposition?

I've limited the question to hydrogen to avoid getting side tracked by possible discussions of electrons being identical particles, but if there is some interesting insight about multielectron atoms that would also be cool.

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  • $\begingroup$ Atoms can be in superpositions of states. I would be carful to call an orbital a state, though. Orbitals are usually thought of as visualizations of the most important chemical aspects of the total wave function of multi-electron atoms and there is no simple way to go from the entire state to an orbital model. For purposes of chemistry this is usually not necessary, which is why the orbital model is a good approximation for chemists. For quantum chemistry and optics one does have to understand the entire state, though. The "what if" part of your question fills entire quantum optics books. $\endgroup$ – CuriousOne Jan 5 '16 at 16:56
  • $\begingroup$ Short answer: Essentially (in principle) yes. Most of the times an electron in a higher level rapidly decays to its lowest level due to many different decoherence mechanisms. Some hyperfine levels of atoms are however quite stable and are routinely used as qubit (see e.g. Ion traps) $\endgroup$ – lcv Jan 5 '16 at 17:47
  • $\begingroup$ @CuriousOne Are orbitals not just simultaneous eigenstates of the Hamiltonian, L^2, and Lz, i.e. solutions to the Schrodinger equation? Granted the filling of orbitals is different than predicted by solving the SE due to relativistic corrections, spin orbit coupling, etc, but... is it not that way for multielectron atoms? $\endgroup$ – SSD Jan 5 '16 at 20:52
  • $\begingroup$ Multi-electron atoms are correctly described by relativistic quantum field theory. I don't know if there is anything like the orbital model in that theory. I have a feeling there may not be. We can, however, approximate the outer electrons reasonably well with the non-relativistic orbitals that make sense for hydrogen for small energy values like the ones that occur in optical interactions and in chemistry. It's a good question... and I admit that I don't have a satisfactory answer beyond my doubts. $\endgroup$ – CuriousOne Jan 5 '16 at 21:50
  • $\begingroup$ @CuriousOne That's ok. I appreciate the answer! Definitely helps. $\endgroup$ – SSD Jan 5 '16 at 23:48
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The Quantum physics answer to this question would be that the nature's reality of matter is vastly difference from our usual perception of matter. In reality, matter is not - something solid, something at a specific location, and something with a specific momentum. Uncertainty principle states that momentum and position of a particle can not both be determined. So, the answer is those 1s, 2s, 2p orbitals are just a prop to give a rough idea about the reality which is more complicated and can perhaps best be obtained from Schrodinger's equation which would give probability distribution of finding the electron at different points in space. Note that different points will have some value of probability, some points higher values than others. So actually, the electron exists over many space locations at the same instant of time with varying probability values for different locations. This is because the reality of nature is radically different than what we using our eyes used to day to day scenario can perceive.

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