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.

The speed of neutrons greatly influences how well they are absorbed by different isotopes.

Bibliography:

Subcase of a normed vector space, therefore also necessarily a vector space.

Does not have any non-trivial normal subgroup.

And therefore, going back to our intuition that due to the fundamental theorem on homomorphisms there is one normal group per homomorphism, a simple group is one that has no non-trivial homomorphisms.

An inner product $x\cdot y$ induces a norm with:

In a vector space, a metric may be induced from a norm by using subtraction:

The partial differential equation of non-relativistic quantum mechanics.

Experiments explained:

Experiments not explained: those that the Dirac equation explains like:

To get some intuition on the equation on the consequences of the equation, have a look at:

The easiest to understand case of the equation which you must have in mind initially that of the Schrödinger equation for a free one dimensional particle.

Then, with that in mind, the general form of the Schrödinger equation is:where:

The $\overrightarrow{x}$ argument of $\psi$ could be anything, e.g.:Note however that there is always a single magical $t$ time variable. This is needed in particular because there is a time partial derivative in the equation, so there must be a corresponding time variable in the function. This makes the equation explicitly non-relativistic.

The general Schrödinger equation can be broken up into a trivial time-dependent and a time-independent Schrödinger equation by separation of variables. So in practice, all we need to solve is the slightly simpler time-independent Schrödinger equation, and the full equation comes out as a result.

Existence and uniqueness: mathoverflow.net/questions/212913/existence-and-uniqueness-for-two-dimensional-time-dependent-schr%C3%B6dinger-equation

TODO how close does it get to Shannon's limit?

physics.stackexchange.com/questions/614757/intuitive-explanation-for-why-time-symmetry-implies-conservation-of-energy on Physics Stack Exchange