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Schrödinger equation solution for the hydrogen atom is a very important subject about which there is a lot to say.
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Articles by others on the same topic
Physics (like all well done science) is the art of predicting the future by modelling the world with mathematics.
Ciro Santilli doesn't know physics. He writes about it partly to start playing with some scientific content for: OurBigBook.com, partly because this stuff is just amazingly beautiful.
Ciro's main intellectual physics fetishes are to learn quantum electrodynamics (understanding the point of Lie groups being a subpart of that) and condensed matter physics.
Every science is Physics in disguise, but the number of objects in the real world is so large that we can't solve the real equations in practice.
Luckily, due to emergence, we can use uglier higher level approximations of the world to solve many problems, with the complex limits of applicability of those approximations.
Therefore, such higher level approximations are highly specialized, and given different names such as:
Unifying those two into the theory of everything one of the major goals of modern physics.
xkcd 435: Fields arranged by purity
. Source. Reductionism comes to mind.