2s/2p energy split in the hydrogen emission spectrum, not predicted by the Dirac equation, but explained by quantum electrodynamics, which is one of the first great triumphs of that theory.
Note that for atoms with multiple electrons, 2s/2p shifts are expected: Why does 2s have less energy than 1s if they have the same principal quantum number?. The surprise was observing that on hydrogen which only has one electron.
Initial experiment: Lamb-Retherford experiment.
On the return from the train from the Shelter Island Conference in New York, Hans Bethe managed to do a non-relativistic calculation of the Lamb shift. He then published as The Electromagnetic Shift of Energy Levels by Hans Bethe (1947) which is still paywalled as of 2021, fuck me: journals.aps.org/pr/abstract/10.1103/PhysRev.72.339 by Physical Review.
The Electromagnetic Shift of Energy Levels Freeman Dyson (1948) published on Physical Review is apparently a relativistic analysis of the same: journals.aps.org/pr/abstract/10.1103/PhysRev.73.617 also paywalled as of 2021.
TODO how do the infinities show up, and how did people solve them?
Lamb shift by Dr. Nissar Ahmad (2020)
Source. Whiteboard Lecture about the phenomena, includes description of the experiment. Seems quite good.www.mdpi.com/2624-8174/2/2/8/pdf History and Some Aspects of the Lamb Shift by G. Jordan Maclay (2019)
Freeman Dyson - The Lamb shift by Web of Stories (1998)
Source. Mentions that he moved to the USA from the United Kingdom specifically because great experiments were being carried at Columbia University, which is where the Lamb-Retherford experiment was done, and that Isidor Isaac Rabi was the head at the time.
He then explains mass renormalization briefly: instead of calculating from scratch, you just compare the raw electron to the bound electron and take the difference. Both of those have infinities in them, but the difference between them cancels out those infinities.
Hans Bethe - The Lamb shift (1996)
Source. Ahh, Hans is so old in that video, it is sad to see. He did live a lot tough. Mentions that the shift is of about 1000 MHz.
The following video: www.youtube.com/watch?v=vZvQg3bkV7s Hans Bethe - Calculating the Lamb shift.
Lamb shift by Vidya-mitra (2018)
Source. Selected Papers on Quantum Electrodynamics by Julian Schwinger (1958) by 
Ciro Santilli 35 Updated 2025-03-08 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-03-08 +Created 1970-01-01Recommended by Ron Maimon at physics.stackexchange.com/questions/18632/good-book-on-the-history-of-quantum-mechanics/18643#18643.
Julian Schwinger's selection of academic papers by himself and others.
Advanced quantum mechanics II by Douglas Gingrich (2004) by Ciro Santilli 35 Updated 2025-03-08 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-03-08 +Created 1970-01-01Using green fluorescent protein as a protein tag.
One dimension in position representation:
In three dimensions In position representation, we define it by using the gradient, and so we see that
Position and Momentum from Wavefunctions by Faculty of Khan (2018)
Source. Proves in detail why the momentum operator is . The starting point is determining the time derivative of the expectation value of the position operator. Organization developing photonic quantum computer by Ciro Santilli 35 Updated 2025-03-08 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-03-08 +Created 1970-01-01 Infinitely many slits thought experiment by Ciro Santilli 35 Updated 2025-03-08 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-03-08 +Created 1970-01-01Thought experiment that illustrates the path integral formulation of quantum field theory.
Mentioned for example in quantum field theory in a nutshell by Anthony Zee (2010) page 8.
PageRank was apparently inspired by it originally, given that.
When you fail a HR interview, then you know you've reached rock bottom.
Investments:
- 2024: 75m GBP
- 2023-04: 15m GBP: www.uktech.news/deep-tech/riverlane-series-b-20230424 At 100 employeed on LinkedIn, this should keep them going for two more years.
- 2022 500k GBP: www.uktech.news/deep-tech/riverlane-rigetti-quantum-innovate-uk-20220628 by Innovate UK for joing project with Rigetti Computing to work on quantum error correction
The Operating System for Quantum Computing by Steve Brierley (2021)
Source. Founding CEO. He seems nice. You might as well just start watching at: youtu.be/ugzWnw1LTBE?t=1166 where more specific things start to come out.Consider the E. Coli K-12 MG1655 operon thrLABC.
That single operon can produce two different mRNA transcription units:
- thrL only, the transcription unit is also called thrL: biocyc.org/ECOLI/NEW-IMAGE?object=TU0-42486
- thrL + thrA + thrB + thrC all together, the transcription unit is called thrLABC: biocyc.org/ECOLI/NEW-IMAGE?type=OPERON&object=TU00178
The reason for this appears to be that there is a rho-independent termination region after thrL. But then under certain conditions, that must get innactivated, and then the thrLABC is produced instead.
This is one of the most canonical examples of "Cult leader Jesus tries to divert faith from an old religion into his own".
Organization developing neutral atom quantum computer by Ciro Santilli 35 Updated 2025-03-08 +Created 1970-01-01
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