Here is a vendor showcasing their device. They claim in that video that a single photon is produced and detected:

Concrete device described at: Video "How to use an SiPM - Experiment Video by SensLTech (2018)".

Amazingly confirms the wave particle duality of quantum mechanics.

The effect is even more remarkable when done with individual particles such individual photons or electrons.

Richard Feynman liked to stress how this experiment can illustrate the core ideas of quantum mechanics. Notably, he night have created the infinitely many slits thought experiment which illustrates the path integral formulation.

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.

There is also a time-energy uncertainty principle, because those two operators are also complementary.

Appears in the Schrödinger equation.

Equals the quantum of angular momentum in the Bohr model.

Do electrons spontaneously jump from high orbitals to lower ones emitting photons?

Explaining this was was one of the key initial achievements of the Dirac equation.

Yes, but this is not predicted by the Schrödinger equation, you need to go to the Dirac equation.

A critical application of this phenomena is laser.

See also:

TODO understand better, mentioned e.g. at Subtle is the Lord by Abraham Pais (1982) page 20, and is something that Einstein worked on.

Spin is one of the defining properties of elementary particles, i.e. number that describes how an elementary particle behaves, much like electric charge and mass.

Possible values are half integer numbers: 0, 1/2, 1, 3/2, and so on.

The approach shown in this section: Section "Spin comes naturally when adding relativity to quantum mechanics" shows what the spin number actually means in general. As shown there, the spin number it is a direct consequence of having the laws of nature be Lorentz invariant. Different spin numbers are just different ways in which this can be achieved as per different Representation of the Lorentz group.

Video 1. "Quantum Mechanics 9a - Photon Spin and Schrodinger's Cat I by ViaScience (2013)" explains nicely how:

Thought experiment that illustrates the path integral formulation of quantum field theory.

Mentioned for example in quantum field theory in a nutshell by Anthony Zee (2010) page 8.

No, but why?

The half-life of radioactive decay, which as discovered a few years before quantum mechanics was discovered and matured, was a major mystery. Why do some nuclei fission in apparently random fashion, while others don't? How is the state of different nuclei different from one another? This is mentioned in Inward Bound by Abraham Pais (1988) Chapter 6.e Why a half-life?

The term also sees use in other areas, notably biology, where e.g. RNAs spontaneously decay as part of the cell's control system, see e.g. mentions in E. Coli Whole Cell Model by Covert Lab.

Ciro Santilli once visited the chemistry department of a world leading university, and the chemists there were obsessed with NMR. They had small benchtop NMR machines. They had larger machines. They had a room full of huge machines. They had them in corridors and on desk tops. Chemists really love that stuff. More precisely, these are used for NMR spectroscopy, which helps identify what a sample is made of.

Basically measures the concentration of certain isotopes in a region of space.