Selection rule Updated 2025-07-16
phys.libretexts.org/Courses/University_of_California_Davis/UCD%3A_Physics_9HE_-_Modern_Physics/06%3A_Emission_and_Absorption_of_Photons/6.2%3A_Selection_Rules_and_Transition_Times has some very good mentions:
So it appears that if a hydrogen atom emits a photon, it not only has to transition between two states whose energy difference matches the energy of the photon, but it is restricted in other ways as well, if its mode of radiation is to be dipole. For example, a hydrogen atom in its 3p state must drop to either the n=1 or n=2 energy level, to make the energy available to the photon. The n=2 energy level is 4-fold degenerate, and including the single n=1 state, the atom has five different states to which it can transition. But three of the states in the n=2 energy level have l=1 (the 2p states), so transitioning to these states does not involve a change in the angular momentum quantum number, and the dipole mode is not available.
So what's the big deal? Why doesn't the hydrogen atom just use a quadrupole or higher-order mode for this transition? It can, but the characteristic time for the dipole mode is so much shorter than that for the higher-order modes, that by the time the atom gets around to transitioning through a higher-order mode, it has usually already done so via dipole. All of this is statistical, of course, meaning that in a large collection of hydrogen atoms, many different modes of transitions will occur, but the vast majority of these will be dipole.
It turns out that examining details of these restrictions introduces a couple more. These come about from the conservation of angular momentum. It turns out that photons have an intrinsic angular momentum (spin) magnitude of , which means whenever a photon (emitted or absorbed) causes a transition in a hydrogen atom, the value of l must change (up or down) by exactly 1. This in turn restricts the changes that can occur to the magnetic quantum number: can change by no more than 1 (it can stay the same). We have dubbed these transition restrictions selection rules, which we summarize as:
Bicycle Updated 2025-07-16
Big Dipper Updated 2025-07-16
Biochemist Updated 2025-07-16
The best Romance of the Three Kingdoms adaptation of all time? Mind blowing.
www.youtube.com/watch?v=e8VWVvHjskM&list=PLIj4BzSwQ-_ueXTO7EBmShk1b3lEqc5b_ official CCTV电视剧 (CCTV TV Series Channel) upload without Chinese + English subtitles.
Video 1.
Title sequence of the Romance of the Three Kingdoms (1994 TV series)
Source. From this you can understand that the number os extras is off the charts!
yEnc Updated 2025-07-16
Little-o notation Updated 2025-07-16
Stronger version of the big O notation, basically means that ratio goes to zero. In big O notation, the ratio does not need to go to zero.
So in informal terms, big O notation means , and little-o notation means .
E.g.:
  • K does not tend to zero
Mesozoic Updated 2025-07-16
Santos, São Paulo, Brazil Updated 2025-07-16
Ciro Santilli lived in Santos from about the year 1998 to 2007, with a 10 month hiatus in Coventry, UK, until he went to the University of São Paulo.
Santos is the nearest beach city to São Paulo City, and for this reason:
Ciro idolizes Santos as the perfect location to live nature-wise due to its amazing wide sandy beach, in which Ciro spent endless hours walking on the sand and on the largest beachfront garden in the world (archive), meditating, and playing some soccer after school was over. Santos is also the city where Pelé first played professionally.
Ciro has visited Santos several times after leaving Brazil. Doing this gives him a weird feeling of having a separate life, in which time passes 2 weeks every few years. Of course, as your family grows, it gets harder and harder to go back home, and your family members might want to just go travel to more interesting places than just stay at your wonderful beach which you love in part due to nostalgia.
Ciro is also fond of the concept of the small public buildings near the beach garden (postos de praia), which serve different cultural activities: library, comic book store, art cinema, surf school. It is such a shame that the library and comic book ones are in such bad shape as of 2020, old books and poor people who go there to sleep a bit in the barely working air conditioning. Ciro fantasizes how those could instead be cultural hubs for the gathering of the brightest artists, and scientists, of town. Maybe they are just too small. Maybe it is not within the realm of possibility of public service. Maybe, we should focus instead in the poorer regions, far form the beach. But the dream remains.
Santos only has one natural defect: mosquitoes. By the sea it is fine because the wind is strong, and they don't like salt water. But anywhere else, you will be eaten alive, and maybe get dengue, Ciro got it once. Gene drive, please.
This instagram page has several drone videos of the region: www.instagram.com/malta.drone
Figure 1.
Panoramic view of Santos' beach line by Diego Torres Silvestre (2009)
Source.
Figure 2.
Canal 5 on the beach by VicTrindade (2017)
Source. This is one of Santos 7 old canals, which are still in use and serve to reduce floodings in the city, which are caused by the strong tropical rains that fall on the city. This is particularly important to keep the mosquito population under some control. All canals were built in the first third of the 20th century, except canal 7 which is from 1968[ref]. The canals have normally very shallow water when it is not raining, and since it is rain water they are basically clean. There are other canals which are/were used for sewage, but then are not open air. The canals now serve as handy reference points and practical avenues in town, as well as being surrounded with nice trees that provide shade and drop small inedible purple fruit that will stain your car for all eternity. They do scar the beach line a bit it must be said, but it's part of the charm of the city, and they serve as good reference points for runners.
The National Byway Updated 2025-07-16
It runs along quiet roads, rather than a mixture of roads and tracks like the National Cycle Network, making it more appropriate for road bikes.
TODO interactive online app? Ahh, those charities that try to make money by individual transactions... when they die, nothing will be left of all their work.
Edit: noticed that it is on by default on OpenStreetMaps web UI under the "Cycle Map" layer marked at "NB".

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