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useCallback Updated 2025-07-16 Quantum mechanics Updated 2025-07-16
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.
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Quantum electrodynamics Lagrangian Updated 2025-07-16
where:
- is the electromagnetic tensor
Note that this is the sum of the:Note that the relationship between and is not explicit. However, if we knew what type of particle we were talking about, e.g. electron, then the knowledge of psi would also give the charge distribution and therefore
- Dirac Lagrangian, which only describes the "inertia of bodies" part of the equation
- the electromagnetic interaction term , which describes term describes forces
As mentioned at the beginning of Quantum Field Theory lecture notes by David Tong (2007):
- by "Lagrangian" we mean Lagrangian density
- the generalized coordinates of the Lagrangian are fields
Bitcoin Core snap Updated 2025-07-16
Officially supported installation method on Ubuntu 23.10.
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Quote by Ciro Santilli Updated 2025-07-16
These are "original" thoughts that Ciro had which at some point in the past amused him. Some would call them pieces of wisdom, others self delusion. All have likely been thought by others in the past, and some of them Ciro thinks to himself after a few years: "why did I like this back then??".
On the theory vs practice of computer science:
Whereas Turing completeness is enough for mathematicians, humans need "run-on-Debian-complete".
On how you make the best friends in life when dealing with hardships together.In Ciro's case, this in particular means going through high school/universities studies and work projects, though of course war would apply particularly well. Perhaps inspired by as iron sharpens iron, so one person sharpens another.
This is of course just another version of one picture is worth a thousand words.
Quantum number Updated 2025-07-16
Quantum numbers appear directly in the Schrödinger equation solution for the hydrogen atom.
However, it very cool that they are actually discovered before the Schrödinger equation, and are present in the Bohr model (principal quantum number) and the Bohr-Sommerfeld model (azimuthal quantum number and magnetic quantum number) of the atom. This must be because they observed direct effects of those numbers in some experiments. TODO which experiments.
E.g. The Quantum Story by Jim Baggott (2011) page 34 mentions:This refers to forbidden mechanism. TODO concrete example, ideally the first one to be noticed. How can you notice this if the energy depends only on the principal quantum number?
As the various lines in the spectrum were identified with different quantum jumps between different orbits, it was soon discovered that not all the possible jumps were appearing. Some lines were missing. For some reason certain jumps were forbidden. An elaborate scheme of ‘selection rules’ was established by Bohr and Sommerfeld to account for those jumps that were allowed and those that were forbidden.
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GitHub awesome repo Updated 2025-07-16
Schrödinger equation solution for the hydrogen atom Updated 2025-07-16
Is the only atom that has a closed form solution, which allows for very good predictions, and gives awesome intuition about the orbitals in general.
It is arguably the most important solution of the Schrodinger equation.
In particular, it predicts:
- the major spectral line of the hydrogen atom by taking the difference between energy levels
The explicit solution can be written in terms of spherical harmonics.
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