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Ciro Santilli often wonders to himself, how much of the natural sciences can one learn in a lifetime? Certainly, a very strong basis, with concrete experimental and physics, chemistry and biology should be attainable to all? How much Ciro manages to learning and teach in those areas is a kind of success metric of Ciro's life.

Everyone is beginner when the field is new, and there is value in tutorials written by beginners.

For example, Ciro Santilli felt it shocking how direct and satisfying Richard Feynman's scientific vulgarization of quantum electrodynamics were, e.g. at: Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979), and that if he had just assumed minimal knowledge of mathematics, he was about to give a full satisfactory picture in just a few hours.

Other supporters of this:

Nature is a black box, right?

You don't need to understand the from first principles derivation of every single phenomena.

And most important of all: you should not start learning phenomena by reading the from first principles derivation.

Instead, you should see what happens in experiments, and how matches some known formula (which hopefully has been derived from first principles).

Only open the boxes (understand from first principles derivation) if the need is felt!

E.g.:

Physics is all about predicting the future. If you can predict the future with an end result, that's already predicting the future, and valid.

The key is to define only the minimum number of measures: if you define more definitions become over constrained and could be inconsistent.

Learning the modern SI is also a great way to learn some interesting Physics.

Had hardware acceleration in mind from the very start, and for a long time that has meant GPU acceleration.

Starting in the 2019 redefinition of the SI base units, the elementary charge is assigned a fixed number, and the Ampere is based on it and on the second, which is beautiful.

This choice is not because we attempt to count individual electrons going through a wire, as it would be far too many to count!

Rather, it is because because there are two crazy quantum mechanical effects that give us macroscopic measures that are directly related to the electron charge. www.nist.gov/si-redefinition/ampere/ampere-quantum-metrology-triangle by the NIST explains that the two effects are:

Those effect work because they also involve dividing by the Planck constant, the fundamental constant of quantum mechanics, which is also tiny, and thus brings values into a much more measurable order of size.

The Schrödinger equation Hamiltonian has to be a Hermitian so we will have only positive energies I think: quantumcomputing.stackexchange.com/questions/12113/why-does-a-hamiltonian-have-to-be-hermitian

This is basically how quantum computing was first theorized by Richard Feynman: quantum computers as experiments that are hard to predict outcomes.

TODO answer that: quantumcomputing.stackexchange.com/questions/5005/why-it-is-hard-to-simulate-a-quantum-device-by-a-classical-devices. A good answer would be with a more physical example of quantum entanglement, e.g. on a photonic quantum computer.

This equation is a subcase of Equation "Schrödinger equation for a one dimensional particle" with $V(x)=x^2$.

We get the time-independent Schrödinger equation by substituting this $V$ into Equation "time-independent Schrödinger equation for a one dimensional particle":

Now, there are two ways to go about this.

The first is the stupid "here's a guess" + "hey this family of solutions forms a complete basis"! This is exactly how we solved the problem at Section "Solving partial differential equations with the Fourier series", except that now the complete basis are the Hermite functions.

The second is the much celebrated ladder operator method.

Examples:

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 explicit solution can be written in terms of spherical harmonics.

Determines energy. This comes out directly from the resolution of the Schrödinger equation solution for the hydrogen atom where we have to set some arbitrary values of energy by separation of variables just like we have to set some arbitrary numbers when solving partial differential equations with the Fourier series. We then just happen to see that only certain integer values are possible to satisfy the equations.

Fixed quantum angular momentum in a given direction.

Can range between $\pm l$.

E.g. consider gallium which is 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p1:

The z component of the quantum angular momentum is simply:so e.g. again for gallium:

Note that this direction is arbitrary, since for a fixed azimuthal quantum number (and therefore fixed total angular momentum), we can only know one direction for sure. $z$ is normally used by convention.