Ciro Santilli @cirosantilli  40

Whole organism simulation of C. elegans.

High level simulation only, no way to get from DNA to worm! :-) Includes:

3D body viewer at: browser.openworm.org/ TODO can you click on a cell to get its name?

If you pass parallel light.

For a biconvex spherical lens, it is given by:where:

We will sometimes just write them without superscript, as it saves typing and is useless.

The principal quantum number thing fully determining energy is only true for the hydrogen emission spectrum for which we can solve the Schrödinger equation explicitly.

For other atoms with more than one electron, the orbital names are just a very good approximation/perturbation, as we don't have an explicit solution. And the internal electrons do change energy levels.

Note however that due to the more complex effect of the Lamb shift from QED, there is actually a very small 2p/2s shift even in hydrogen.

Looking at the energy level of the Schrödinger equation solution for the hydrogen atom, you would guess that for multi-electron atoms that only the principal quantum number would matter, azimuthal quantum number getting filled randomly.

However, orbitals energies for large atoms don't increase in energy like those of hydrogen due to electron-electron interactions.

In particular, the following would not be naively expected:

This rule is only an approximation, there exist exceptions to the Madelung energy ordering rule.

Bibliography:

This notation is so confusing! People often don't manage to explain the intuition behind it, why this is an useful notation. When you see Indian university entry exam level memorization classes about this, it makes you want to cry.

The key reason why term symbols matter are Hund's rules, which allow us to predict with some accuracy which electron configurations of those states has more energy than the other.

web.chem.ucsb.edu/~devries/chem218/Term%20symbols.pdf puts it well: electron configuration notation is not specific enough, as each such notation e.g. 1s2 2s2 2p2 contains several options of spins and z angular momentum. And those affect energy.

This is why those symbols are often used when talking about energy differences: they specify more precisely which levels you are talking about.

Basically, each term symbol appears to represent a group of possible electron configurations with a given quantum angular momentum.

We first fix the energy level by saying at which orbital each electron can be (hyperfine structure is ignored). It doesn't even have to be the ground state: we can make some electrons excited at will.

The best thing to learn this is likely to draw out all the possible configurations explicitly, and then understand what is the term symbol for each possible configuration, see e.g. term symbols for carbon ground state.

It also confusing how uppercase letters S, P and D are used, when they do not refer to orbitals s, p and d, but rather to states which have the same angular momentum as individual electrons in those states.

It is also very confusing how extremelly close it looks to spectroscopic notation!

The form of the term symbol is:

The $2S+1$ can be understood directly as the degeneracy, how many configurations we have in that state.

Bibliography:

One of the most beautiful molecular machines known!

The first one with such complexity that was uncovered.

The thing rotates like a water wheel for God's sake, except it uses protons instead of water.

The ATP synthase complex is so large that Power, Sex, Suicide by Nick Lane (2006) page 123 contains a cryoEM image of several ATP synthases on small membrane vesicles, this is the paper: pubs.acs.org/doi/abs/10.1021/bi00437a031# under a fucking paywall.

Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979) mentions it several times.

This was one of the first two great successes of quantum electrodynamics, the other one being the Lamb shift.

In youtu.be/UKbp85zpdcY?t=52 from freeman Dyson Web of Stories interview (1998) Dyson mentions that the original key experiment was from Kusch and Foley from Columbia University, and that in 1948, Julian Schwinger reached the correct value from his calculations.

Apparently first published at The Magnetic Moment of the Electron by Kusch and Foley (1948).

Bibliography:

Gaussian path integrals.