Ciro Santilli @cirosantilli 40

Metric space but where the distance between two distinct points can be zero.

Notable example: Minkowski space.

A matrix that equals its transpose:

Can represent a symmetric bilinear form as shown at matrix representation of a symmetric bilinear form, or a quadratic form.

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

This one is not generally seen by software, which mostly operates starting from OSI layer 2.

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