Examples:

Discrete quantum system model that can model both spin in the Stern-Gerlach experiment or photon polarization in polarizer.

Also known in quantum computing as a qubit :-)

This operator case is surprisingly not necessarily mathematically trivial to describe formally because you often end up getting into the Dirac delta functions/continuous spectrum: as mentioned at: mathematical formulation of quantum mechanics

Basically the operators are just analogous to the classical ones e.g. the classical:becomes:

Besides the angular momentum in each direction, we also have the total angular momentum:

Then you have to understand what each one of those does to the each atomic orbital:

There is an uncertainty principle between the x, y and z angular momentums, we can only measure one of them with certainty at a time. Video 1. "Quantum Mechanics 7a - Angular Momentum I by ViaScience (2013)" justifies this intuitively by mentioning that this is analogous to precession: if you try to measure electrons e.g. with the Zeeman effect the precess on the other directions which you end up modifing.

TODO experiment. Likely Zeeman effect.

Deterministic, but non-local.

Photon hits excited electron, makes that electron go down, and generates a new identical photon in the process, with the exact same:This is the basis of lasers.

Bibliography:

Second quantization also appears to be useful not only for relativistic quantum mechanics, but also for condensed matter physics. The reason is that the basis idea is to use the number occupation basis. This basis is:

Bibliography:

Gaussian path integrals.

True art cannot be consumed in mobile format.

First install NVM/NPM as shown at and then:

Knock knock.

Others:

Discrete quantum effect observed in superconductors with a small insulating layer, a device known as a Josephson junction.

To understand the behaviour effect, it is important to look at the Josephson equations consider the following Josephson effect regimes separately:

A good summary from Wikipedia by physicist Andrew Whitaker:

Bibliography:

TODO is there any relationship between this and the Josephson effect?

Experimental observation published as Experimental Evidence for Quantized Flux in Superconducting Cylinders.

This appears to happen to any superconducting loop, because the superconducting wave function has to be continuous.

Video "Superconducting Qubit by NTT SCL (2015)" suggests that anything in between gets cancelled out by a superposition of current in both directions.

One important quantum mechanics experiment, which using quantum effects explain the dependency of specific heat capacity on temperature, an effect which is not present in the Dulong-Petit law.

This is the solid-state analogue to the black-body radiation problem. It is also therefore a quantum mechanics-specific phenomenon.