Timeline for Is there a good mathematical explanation for why orbital lengths in the periodic table are perfect squares doubled?
Current License: CC BY-SA 4.0
10 events
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| Mar 25, 2022 at 19:47 | history | edited | Aaron Bergman | CC BY-SA 4.0 |
Fixed grammar
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| Mar 25, 2022 at 17:18 | history | edited | Aaron Bergman | CC BY-SA 4.0 |
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| S Mar 25, 2022 at 3:17 | history | suggested | CommunityBot | CC BY-SA 4.0 |
some typesetting corrections
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| Mar 24, 2022 at 23:40 | review | Suggested edits | |||
| S Mar 25, 2022 at 3:17 | |||||
| Mar 24, 2022 at 20:19 | history | edited | Aaron Bergman | CC BY-SA 4.0 |
added 1 character in body
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| Mar 24, 2022 at 1:18 | comment | added | Eugene Stern | Thanks! I have to think about the $SO(4)$ action in a quiet room for a few minutes, but something like "the $n^2$-dimensional space is an irreducible representation of a larger set of symmetries" is totally the kind of answer I was hoping for. | |
| Mar 24, 2022 at 1:16 | vote | accept | Eugene Stern | ||
| Mar 22, 2022 at 19:26 | comment | added | Aaron Bergman | Sure. This is only intended to give the "more conceptual explanation" for the appearance of $2n^2$ in the Hydrogen atom. Multiple electrons are hard. | |
| Mar 22, 2022 at 13:53 | comment | added | Carlo Beenakker | the key problem I see is how to extend this argument for the hydrogen atom (one electron in a 1/r potential), to atoms containing multiple electrons (which will interact with the core as well as with themselves); this extension would then need to explain how the $n$ ordering rule becomes the $n+l$ ordering rule (and thus the sequence 2,8,18,32,... becomes 2,8,8,18,18,...); one of the papers I cite invokes the chain SO(4,2) $\rightarrow$ SO(3,2) $\rightarrow$ SO(3) $\otimes$ SO(2) to arrive at the $n+l$ rule, no idea if that makes sense or not. | |
| Mar 22, 2022 at 13:31 | history | answered | Aaron Bergman | CC BY-SA 4.0 |