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Qmechanic ♦
Qmechanic ♦
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I was wondering, if you wanted to write down the exact expression for electron energies in a hydrogen atom, what would you have to include?

There's principal splitting, fine structure and hyperfine splitting if we don't include external fields, that should be it, right?

For external magnetic/electric fields, there's the Zeeman/Stark effect and for gravity, presumably gravitational tidal splitting.

Would that make it exact? Where would you start from if you wanted to make it as exact as possible, maybe even including some low-order quantum gravity corrections?

Of course, I understand that this is useless for all practical purposes and the scales you'd have to include would be wildly different, but how would we do it in principle? Are there any known results?

I was wondering, if you wanted to write down the exact expression for electron energies in a hydrogen atom, what would you have to include?

There's principal splitting, fine structure and hyperfine splitting if we don't include external fields, that should be it, right?

For external magnetic/electric fields, there's the Zeeman/Stark effect and for gravity, presumably gravitational tidal splitting.

Would that make it exact? Where would you start from if you wanted to make it as exact as possible, maybe even including some low-order quantum gravity corrections?

Of course, I understand that this is useless for all practical purposes and the scales you'd have to include would be wildly different, but how would we do it in principle? Are there any known results?

I was wondering, if you wanted to write down the exact expression for electron energies in a hydrogen atom, what would you have to include?

There's principal splitting, fine structure and hyperfine splitting if we don't include external fields, that should be it, right?

For external magnetic/electric fields, there's the Zeeman/Stark effect and for gravity, presumably gravitational tidal splitting.

Would that make it exact? Where would you start from if you wanted to make it as exact as possible, maybe even including some low-order quantum gravity corrections?

Of course, I understand that this is useless for all practical purposes and the scales you'd have to include would be wildly different, but how would we do it in principle? Are there any known results?

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user20250
user20250

Exact electron energy levels in hydrogen

I was wondering, if you wanted to write down the exact expression for electron energies in a hydrogen atom, what would you have to include?

There's principal splitting, fine structure and hyperfine splitting if we don't include external fields, that should be it, right?

For external magnetic/electric fields, there's the Zeeman/Stark effect and for gravity, presumably gravitational tidal splitting.

Would that make it exact? Where would you start from if you wanted to make it as exact as possible, maybe even including some low-order quantum gravity corrections?

Of course, I understand that this is useless for all practical purposes and the scales you'd have to include would be wildly different, but how would we do it in principle? Are there any known results?