PostgreSQL spatial index Updated 2025-07-16
Postgraduate education Updated 2025-07-16
Position representation Updated 2025-07-16
A way to write the wavefunction such that the position operator is:i.e., a function that takes the wavefunction as input, and outputs another function:
If you believe that mathematicians took care of continuous spectrum for us and that everything just works, the most concrete and direct thing that this representation tells us is that:equals:
the probability of finding a particle between and at time
Position and momentum space Updated 2025-07-16
One of the main reasons why physicists are obsessed by this topic is that position and momentum are mapped to the phase space coordinates of Hamiltonian mechanics, which appear in the matrix mechanics formulation of quantum mechanics, which offers insight into the theory, particularly when generalizing to relativistic quantum mechanics.
One way to think is: what is the definition of space space? It is a way to write the wave function such that:And then, what is the definition of momentum space? It is of course a way to write the wave function such that:
- the position operator is the multiplication by
- the momentum operator is the derivative by
- the momentum operator is the multiplication by
physics.stackexchange.com/questions/39442/intuitive-explanation-of-why-momentum-is-the-fourier-transform-variable-of-posit/39508#39508 gives the best idea intuitive idea: the Fourier transform writes a function as a (continuous) sum of plane waves, and each plane wave has a fixed momentum.
Bibliography:
Porn vlog Updated 2025-12-13
This is a porn style defined by Ciro Santilli as:
Ciro believes that this is an interesting type of pornography, as it feels more natural and humane than all the horrible trash that comes out of horrendous professional mainstream porn industry.
Yes, it could go down the YouTube/Instagram alley, and lead the vloggers to do things they wouldn't normally do because of the audience. But who is to say that Ciro Santilli doesn't do the same on Stack Overflow to some extent?
That type of porn requires some big courage to make. Or balls if you will. Kudos to those creators, as it is so taboo it could greatly impact their future job prospects.
The travel sex vlog appears to be the most popular way to do it. Presumably the reason being that you would not be able to interact with people in a normal job, so to keep things interesting you need to go to some random places.
Examples:
- twitter.com/JamesWithLola also a travel sex vlog, also French. Hum.
Polyphyly Updated 2025-07-16
Basically mean that parallel evolution happened. Some cool ones:
- homeothermy: mammals and birds
- animal flight: bats, birds and insects
- multicellularity: evolved a bunch of times
Polynomial over a field Updated 2025-07-16
However, a polynomial can be defined over any other field just as well, the most notable example being that of a polynomial over a finite field.
For example, given the finite field of order 9, and with elements , we can denote polynomials over that ring aswhere is the variable name.
For example, one such polynomial could be:and another one:Note how all the coefficients are members of the finite field we chose.
Polykarp Kusch Updated 2025-07-16
Politics Updated 2025-07-16
Political parties in the United States Updated 2025-07-16
Polarity symbols Updated 2025-07-16
Pokemon Updated 2025-07-16
One of the main children cartoons Ciro Santilli liked to watch. Part of the Pokemon Mania of the 90s of course.
Ciro could not understand why Nintendo won't make a proper 3D MMORPG Pokemon with actually 3D Pokemon roaming the land, which is obviously what everyone wants. There are even fan games getting there!until this explaiend it beautifully Video 1. "The Downfall Of Mainline Pokemon Games by GONZ media (2020)":
- pokemon-mmo-3d.com Interesting concept here, where when you deploy a Pokemon, you start controlling the Pokemon rather than the main character
- www.quora.com/Why-won-t-Nintendo-make-an-open-world-3D-Pokémon-RPG/answer/Ciro-Santilli
Poisson's equation Updated 2025-07-16
Generalization of Laplace's equation where the value is not necessarily 0.
Point groups in three dimensions Updated 2025-07-16
Point group Updated 2025-07-16
Point-contact transistor Updated 2025-07-16
As the name suggests, this is not very sturdy, and was quickly replaced by bipolar junction transistor.
Poincaré group Updated 2025-07-16
Full set of all possible special relativity symmetries:
In simple and concrete terms. Suppose you observe N particles following different trajectories in Spacetime.
There are two observers traveling at constant speed relative to each other, and so they see different trajectories for those particles:Note that the first two types of transformation are exactly the non-relativistic Galilean transformations.
- space and time shifts, because their space origin and time origin (time they consider 0, i.e. when they started their timers) are not synchronized. This can be modelled with a 4-vector addition.
- their space axes are rotated relative to one another. This can be modelled with a 4x4 matrix multiplication.
- and they are moving relative to each other, which leads to the usual spacetime interactions of special relativity. Also modelled with a 4x4 matrix multiplication.
The Poincare group is the set of all matrices such that such a relationship like this exists between two frames of reference.
Platform game Updated 2025-07-16
Plane wave function Updated 2025-07-16
In this solution of the Schrödinger equation, by the uncertainty principle, position is completely unknown (the particle could be anywhere in space), and momentum (and therefore, energy) is perfectly known.
The plane wave function appears for example in the solution of the Schrödinger equation for a free one dimensional particle. This makes sense, because when solving with the time-independent Schrödinger equation, we do separation of variable on fixed energy levels explicitly, and the plane wave solutions are exactly fixed energy level ones.
Planck's law Updated 2025-07-16
Used to explain the black-body radiation experiment.
Published as: On the Theory of the Energy Distribution Law of the Normal Spectrum by Max Planck (1900).
The Quantum Story by Jim Baggott (2011) page 9 mentions that Planck apparently immediately recognized that Planck constant was a new fundamental physical constant, and could have potential applications in the definition of the system of units (TODO where was that published):This was a visionary insight, and was finally realized in the 2019 redefinition of the SI base units.
Planck wrote that the constants offered: 'the possibility of establishing units of length, mass, time and temperature which are independent of specific bodies or materials and which necessarily maintain their meaning for all time and for all civilizations, even those which are extraterrestrial and nonhuman, constants which therefore can be called "fundamental physical units of measurement".'
TODO how can it be derived from theoretical principles alone? There is one derivation at; en.wikipedia.org/wiki/Planck%27s_law#Derivation but it does not seem to mention the Schrödinger equation at all.
There are unlisted articles, also show them or only show them.