Fixed total angular momentum.

The direction however is not specified by this number.

To determine the quantum angular momentum, we need the magnetic quantum number, which then selects which orbital exactly we are talking about.

www-thphys.physics.ox.ac.uk/people/AndreiStarinets/sr_mt_2022.html (archive) contains 2022 problem sets and notes, well done Mr Andrei Starinets!

www-pnp.physics.ox.ac.uk/~barra/teaching.shtml As of 2023, contains some good 2015 materials: web.archive.org/web/20220525094139/http://www-pnp.physics.ox.ac.uk/~barra/teaching.shtml It was called "Subatomic physics" back then.

2015 professor: Alan J. Barr.

Possible 2022 professor: Guy Wilkinson (unconfirmed): www.chch.ox.ac.uk/staff/professor-guy-wilkinson

This was the original name of Google Search.

One wonders if this name has some influence from the LGBT culture in San Francisco! The sexual innuendo is palpable.

"Back" is of course a reference to "backlinks", since Google Search relies on incoming links (AKA backlinks) to a webpage to determine its importance.

Pseudo-fuck.

Only present in Gram-negative bacteria.

Many bad films have good aspects. They just didn't cross the elusive threshold of a good film.

An example where SELECT FOR UPDATE is a good solution to an use case can be seen at: nodejs/sequelize/raw/parallel_select_and_update.js.

SELECT FOR UPDATE vs/together with the SQL transaction isolation level is commented at: stackoverflow.com/questions/10935850/when-to-use-select-for-update.

The opposite of quasiparticle, see notaby: quasiparticles vs elementary particles.

As per en.wikipedia.org/w/index.php?title=Semidirect_product&oldid=1040813965#Properties, unlike the Direct product, the semidirect product of two goups is neither unique, nor does it always exist, and there is no known algorithmic way way to tell if one exists or not.

This is because reaching the "output" of the semidirect produt of two groups requires extra non-obvious information that might not exist. This is because the semi-direct product is based on the product of group subsets. So you start with two small and completely independent groups, and it is not obvious how to join them up, i.e. how to define the group operation of the product group that is compatible with that of the two smaller input groups. Contrast this with the Direct product, where the composition is simple: just use the group operation of each group on either side.

Product of group subsets

So in other words, it is not a function like the Direct product. The semidiret product is therefore more like a property of three groups.

The semidirect product is more general than the direct product of groups when thinking about the group extension problem, because with the direct product of groups, both subgroups of the larger group are necessarily also normal (trivial projection group homomorphism on either side), while for the semidirect product, only one of them does.

Conversely, en.wikipedia.org/w/index.php?title=Semidirect_product&oldid=1040813965 explains that if $G=N⋊H$, and besides the implied requirement that N is normal, H is also normal, then $G=N\times H$.

Smallest example: $D_6=C_3⋊C_2$ where $D$ is a dihedral group and $C$ are cyclic groups. $C_3$ (the rotation) is a normal subgroup of $D_6$, but $C_2$ (the flip) is not.

Note that with the Direct product instead we get $C_6$ and not $D_6$, i.e. $C_3\times C_2=C_6$ as per the direct product of two cyclic groups of coprime order is another cyclic group.

TODO:

Bibliography: math.stackexchange.com/questions/1726939/is-this-intuition-for-the-semidirect-product-of-groups-correct