Energy Eigenstates: Can Electron in Hydrogen Atom?

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An electron in a hydrogen atom can indeed exist in an energy eigenstate, particularly when the atom is isolated from external interactions. In such a scenario, measuring the electron's energy will confirm that it occupies a specific energy level, thus qualifying as an energy eigenstate. However, in practical situations, hydrogen atoms often interact with one another, forming diatomic molecules, which alters their energy states. The covalent bond in these diatomic hydrogen molecules is relatively weak, allowing for reactivity under certain conditions. Therefore, while an isolated hydrogen atom's electron can be in an energy eigenstate, this is less common in molecular contexts.
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Can an electron in a hydrogen atom every been in an energy eigenstate?
 
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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.
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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