Can an electron in a hydrogen atom every been in an energy eigenstate?
Well, I'm trying to get something from your inaccurate English wording and give you this answer: typically, it's very unlikely to meet a single, isolated H-atom. Usually H-atoms, when more than 1, tend to couple with each other and form a diatomic stable molecule. The energy eigenstates (point spectrum) of the single atom are not energy eigenstates of the molecular Hamiltonian anymore. What chemists call the sigma covalent bond between the 2 H atoms is not that strong and this molecule can react with other molecules, when certain exterior (pressure & temperature) conditions are met.
Sorry about my english. I had meant to ask whether an electron in a hydrogen atom can *ever* be in an energy eigenstate ie whether an electron can exist in a single orbital alone. Ifr the question still doesn't make sense, then I've probably gone and confused myself about something...
The electron is only one, so it can occupy any energy level it wants to.
Well, if you take a Hydrogen atom, isolated from everything else (in terms of interaction) and then measure the electron's energy, it will be in an energy eigenstate after the measurement.
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