Ciro Santilli @cirosantilli 37

TODO understand better, mentioned e.g. at Subtle is the Lord by Abraham Pais (1982) page 20, and is something that Einstein worked on.

More interestingly, how is that implied by the Stern-Gerlach experiment?

physics.stackexchange.com/questions/266359/when-we-say-electron-spin-is-1-2-what-exactly-does-it-mean-1-2-of-what/266371#266371 suggests that half could either mean:

This example covered for example at Video 1. "Term Symbols Example 1 by TMP Chem (2015)".

Carbon has electronic structure 1s2 2s2 2p2.

For term symbols we only care about unfilled layers, because in every filled layer the total z angular momentum is 0, as one electron necessarily cancels out each other:

So in this case, we only care about the 2 electrons in 2p2. Let's list out all possible ways in which the 2p2 electrons can be.

There are 3 p orbitals, with three different magnetic quantum numbers, each representing a different possible z quantum angular momentum.

We are going to distribute 2 electrons with 2 different spins across them. All the possible distributions that don't violate the Pauli exclusion principle are:

m_l  +1  0 -1  m_L  m_S
     u_ u_ __    1    1
     u_ __ u_    0    1
     __ u_ u_   -1    1
     d_ d_ __    1   -1
     d_ __ d_    0   -1
     __ d_ d_   -1   -1
     u_ d_ __    1    0
     d_ u_ __    1    0
     u_ __ d_    0    0
     d_ __ u_    0    0
     __ u_ d_   -1    0
     __ d_ u_   -1    0
     ud __ __    2    0
     __ ud __    0    0
     __ __ ud   -2    0

where:

For example, on the first line:we have:and so the sum of them has angular momentum $0+1\hslash =1\hslash$. So the value of $m_L$ is 1, we just omit the $\hslash$.

TODO now I don't understand the logic behind the next steps... I understand how to mechanically do them, but what do they mean? Can you determine the term symbol for individual microstates at all? Or do you have to group them to get the answer? Since there are multiple choices in some steps, it appears that you can't assign a specific term symbol to an individual microstate. And it has something to do with the Slater determinant. The previous lecture mentions it: www.youtube.com/watch?v=7_8n1TS-8Y0 more precisely youtu.be/7_8n1TS-8Y0?t=2268 about carbon.

youtu.be/DAgEmLWpYjs?t=2675 mentions that ${}^{3}D$ is not allowed because it would imply $L=2,S=1$, which would be a state uu __ __ which violates the Pauli exclusion principle, and so was not listed on our list of 15 states.

He then goes for ${}^{1}D$ and mentions:and so that corresponds to states on our list:Note that for some we had a two choices, so we just pick any one of them and tick them off off from the table, which now looks like:

Then for ${}^{3}P$ the choices are:so we have 9 possibilities for both together. We again verify that 9 such states are left matching those criteria, and tick them off, and so on.

For the $m_S$, we have two electrons with spin up. The angular momentum of each electron is $1/2\hslash$, and so given that we have two, the total is $1\hslash$, so again we omit $\hslash$ and $m_S$ is 1.

Bibliography:

Ciro Santilli is against all affirmative action, except for one: giving amazing free eduction to the poor.

Notably, Ciro is against university entry quotas.

The basic experiment for a photonic quantum computer.

Can be achieved in two ways it seems:

Animation of Hong-Ou-Mandel Effect on a silicon like structure by Quantum Light University of Sheffield (2014): www.youtube.com/watch?v=ld2r2IMt4vg No maths, but gives the result clear: the photons are always on the same side.

Genes list: www.ncbi.nlm.nih.gov/nuccore/MN908947.3

Some are named after the encoded protein. Others that are not as clean are just orfXXX for open reading frame XXX.

Basically a synonym for second quantization.

tx 243dea31863e94dc2f293489db02452e9bde279df1ab7feb6e456a4af672156a contains another upload script. The help reads:

The script is: github.com/petertodd/python-bitcoinlib/blob/master/examples/publish-text.py

Experimental setup to observe radiation pressure in the laboratory.

Era of quantum computing before we reach physical errors small enough to do perfect quantum error correction as demonstrated by the quantum threshold theorem.

45 1 hour lessons. The Indian traditional music opening is the best.

Author: David Tong.

Number of pages circa 2021: 155.

It should also be noted that those notes are still being updated circa 2020 much after original publication. But without Git to track the LaTeX, it is hard to be sure how much. We'll get there one day, one day.

Likely used at: David Tong's 2009 Quantum Field Theory lectures at the Perimeter Institute.

Some quotes self describing the work:

A follow up course in the University of Cambridge seems to be the "Advanced QFT course" (AQFT, Quantum field theory II) by David Skinner: www.damtp.cam.ac.uk/user/dbs26/AQFT.html

Author: en.wikipedia.org/wiki/Anthony_Zee from University of California, Santa Barbara.

ISBN-13: 978-0691140346

Amazon: www.amazon.com/dp/0691140340

lecture 1 mentions that this book is quick and dirty, as one might guess from the title. Ciro Santilli thinks he's gonna like this one.

First edition: from 2003, www.amazon.com/dp/0691010196, ISBN-13: 978-0691010199.

Summary:

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?

www.mdpi.com/2624-8174/2/2/8/pdf History and Some Aspects of the Lamb Shift by G. Jordan Maclay (2019)

Recommended 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.