# Is $1s2s$ state an upper bound of Helium excited states? [closed]

Generally people says that the state $$1s(1)2s(1)$$ $$^1S$$ is an excited state of Helium atom . Variation theorem guaranties that the expectation value of this state is greater than the ground state, that is $$E[(1s(1)2s(1)]\geq e_0$$ where $$e_0$$ is the ground state energy. For example since $$1s(2)$$ $$^1S$$ is the ground state we can show that the state $$1s(1)2s(1)$$ $$^3S$$ is an upper bound of the first excited state of Helium.

Now let $$e_1$$ be the first excited state of the Helium atom, is there any theorem that guaranties that we have $$E[(1s(1)2s(1) ^1S ]\geq e_1$$ ?

• Which state do you mean, the singlet of the triplet? – my2cts Nov 9 '20 at 13:08
• I mean a Singlet – amilton moreira Nov 9 '20 at 13:08
• The triplet 1s2s state is the lowest excited state. See physics.nist.gov/cgi-bin/ASD/… – my2cts Nov 9 '20 at 13:11
• I know that triplet state is the lowest excited state. I am not asking if singlet sate is the lowest am asking if it is un upper bound of the excite states of helium – amilton moreira Nov 9 '20 at 13:14
• "assuming that $1s(2)$ $^1S$ is the ground state " This is not an assumption but a hard fact. – my2cts Nov 9 '20 at 13:33

## 2 Answers

There is no such theorem. What you have is experimental data and very accurate quantum chemical simulation (any atom with more than 1 electron for some reason is chemistry). There are many more excited states and the singlet certainly is not the highest of these. You could learn a lot by looking at the complete He I level set at https://physics.nist.gov/cgi-bin/ASD/energy1.pl?encodedlist=XXT2&de=0&spectrum=He+I&submit=Retrieve+Data&units=1&format=0&output=0&page_size=15&multiplet_ordered=0&conf_out=on&term_out=on&level_out=on&unc_out=1&j_out=on&lande_out=on&perc_out=on&biblio=on&temp=

• We can proof for example that the triplet is a upper bound of excited states assuming that singlet is a ground state – amilton moreira Nov 9 '20 at 13:16
• @amiltonmoreira I get the impression that you limit yourself to the 1s2s configuration. – my2cts Nov 9 '20 at 13:31
• I am not understanding what you mean – amilton moreira Nov 9 '20 at 13:32
• @amiltonmoreira There are many excited states higher that the 1s2s triplet or singlet. Did you take a look at the NIST database? – my2cts Nov 9 '20 at 13:39
• @amiltonmoreira Theory and experiment essentially give the same answers here. Besides, all physicists are interested in experimental data. – my2cts Nov 9 '20 at 13:56

Yes, according to Wikipedia it is known as the Aufbau principle (or Madelung rule, as I've been taught in school).

• that is not a theorem – amilton moreira Nov 9 '20 at 12:58
• Indeed it is not. By definition theorem is a general proposition not self-evident but proved by a chain of reasoning; a truth established by means of accepted truths. This principle, however is empirically measured, not theoretically postulated. – Krumuvecis Nov 9 '20 at 13:10