Quantum mechanics is quite a broad term. Perhaps it is best to start approaching it from the division into:
- non-relativistic quantum mechanics: obviously the simpler one, and where you should start
- relativistic quantum mechanics: more advanced, and arguably "less useful"
Key experiments that could not work without quantum mechanics: Section "Quantum mechanics experiment".
Mathematics: there are a few models of increasing precision which could all be called "quantum mechanics":
Ciro Santilli feels that the largest technological revolutions since the 1950's have been quantum related, and will continue to be for a while, from deeper understanding of chemistry and materials to quantum computing, understanding and controlling quantum systems is where the most interesting frontier of technology lies.
In many important applications, what you have to solve is not just a single partial differential equation, but multiple partial differential equations coupled to each other. This is the case for many key PDEs including:
Existence and uniqueness of solutions of ordinary differential equations by 
Ciro Santilli 37 Updated 2025-07-16
Ciro Santilli 37 Updated 2025-07-16The Holy Hand Grenade of Antioch scene from Monty Python and the Holy Grail
. Source. When a young Ciro Santilli played Worms Armageddon, he almost shat himself of laughter when he first threw a Holy Grenade. Little did he know it was actually a Monty Python reference.You need separate accounts for different countries: money.stackexchange.com/questions/73361/two-banks-in-two-countries-is-it-possible-to-have-a-unique-paypal-account it's a pain.
The Insane Engineering of DLP by Zack Freedman (2022)
Source. This idealization does not seems to be possible at all in the context of Maxwell's equations with pointlike particles.
No open signup it seems. TODO CV of owner.
They are making a proof assistant to integrate into the website: github.com/bookofproofs/fpl/, reminds Ciro Santilli of website front-end for a mathematical formal proof system.
Joe Corneli, of of the contributors, mentions this in a cool-sounding "Peeragogy" context at metameso.org/~joe/:
I earned my doctorate at The Open University in Milton Keynes, with a thesis focused on peer produced support for peer learning in the mathematics domain. The main case study was planetmath.org; the ideas also informed the development of “Peeragogy”.
Collection of coordinate charts.
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