I had a bit of computer problems lately, my oldest computer did not allow me to enter the BIOS and as such I could not tell from what hard disk to boot and that was the end of the motherboard in that old computer. It was my last Windows XP computer and looking at the latest Windows 7, 10 or 11 stuff there is not that much progress. Windows OS systems become more and more a fashion thing because most of it is outdeveloped and hard to improve upon… But lets go to this small post about the long title above: total angular momentum.
To put it simple: In an atom or molecule with unpaired electrons in it physics people often think of the spin of the unpaired electrons as vectors that get projected against the vertical direction if a magnetic field is applied. Those projections are treated as scalars and as you might have guessed it is either +1/2 or -1/2. (Here I leave the constant of Planck out for simplicity.)
Ok my version of magnetism is that electrons are magnetic monopoles so they have either a north pole charge or a south pole magnetic charge. Adding these up works just like adding up the electrical charges in an atom or a molecule; because after the humble opinion of your servant electron magnetism looks just like electron electricity: permanent and monopole.
So that is all to know, basically it is very simple once you have seen a few times what they do and mean with that “Total angular momentum in the x-direction” because that sounds so complicated. But all in all the calculations they do are just like adding up monopole magnetic charges so they were on the right track more or less a long time ago.
This post is four pictures and for me that is a bit hard because I always made the backgrounds on the computer that broke down. And that old graphics program can’t run on Windows 7 or higher while modern graphics programs like GIMP just don’t have the features to make such a background in a few clicks. Of course a long time ago this doomsday day was foreseen and I saved a lot of backgrounds as png files. So I opened that folder and what? It’s fucking empty…:(
Well lets go to the pictures:
The most hilaric picture is the fourth one where two electrons with opposite spins are in different energy levels in an atom or molecule. And if you want your electron spin as a vector, how the hell should you get opposite pointing vectors while the electrons are in different parts of the atom or molecule? That is very weird behavior and as such it always goes unexplained to the extend it is never mentioned as a problem. Just like all that other stuff that is wrong with electron magnetism as you view them as tiny magnets and not as magnetic monopoles.
Well thanks for your attention and see you in another post.