The Schrödinger equation is not relativistic by Ciro Santilli 37 Updated +Created
Video 1.
Why Relativity Breaks the Schrodinger Equation by Richard Behiel (2023)
Source. Take a plane wave function, because we know its momentum perfectly. Apply a constant voltage to an electron. You can easily bring it beyond the speed of light at about 255.5 keV.
Superconductor resistivity experiment video by Ciro Santilli 37 Updated +Created
Video 1.
Superconductor, 4-probe measurement by Frederiksen Scientific A/S (2015)
Source. OK experiment, illustrates the educational kit they sell. No temperature control, just dumps liquid nitrogen into conductor and watches it drop. But not too bad either. The kit sale link is broken (obviously, enterprise stuff), but there are no archives unfortunately. But it must be some High-temperature superconductor
Waring-Goldbach problem by Ciro Santilli 37 Updated +Created
It is exactly what you'd expect from the name, Waring was watching Netflix with Goldbach, when they suddenly came up with this.
Preprint by Ciro Santilli 37 Updated +Created
Svengali by Ciro Santilli 37 Updated +Created
System call by Ciro Santilli 37 Updated +Created
Berkeley Software Distribution by Ciro Santilli 37 Updated +Created
Legal issues stalled them at the turning point of the Internet, and Linux won. Can't change history.
Did Apple just fork it and made Mac OS X without giving anything back?
Step response of the series RC circuit by Ciro Santilli 37 Updated +Created
This is what happens when you apply a step voltage to a series RC circuit: TODO graph.
Heavyside step function by Ciro Santilli 37 Updated +Created
Ruth Lawrence by Ciro Santilli 37 Updated +Created
en.wikipedia.org/wiki/Ruth_Lawrence
When Lawrence was five, her father gave up his job so that he could educate her at home.
At Oxford, her father continued to be actively involved in her education, accompanying her to all lectures and some tutorials. Lawrence completed her bachelor's degree in two years, instead of the normal three, and graduated in 1985 at the age of 13 with a starred first and special commendation.
www.dailymail.co.uk/femail/article-3713768/Haunting-lesson-today-s-TV-child-geniuses-Ruth-Lawrence-Britain-s-famous-prodigy-tracked-father-drove-heard-troubling-tale.html
he had tried it once before - with an older daughter, Sarah, one of three children he had by a previous marriage.
That experiment ended after he separated from Sarah's increasingly concerned mother, Jutta. He soon found a woman more in tune with his radical ideas in his next spouse, Sylvia Greybourne
Discrete logarithm of the cyclic group by Ciro Santilli 37 Updated +Created
This is the discrete logarithm problem where the group is a cyclic group.
In this case, the problem becomes equivalent to reversing modular exponentiation.
This computational problem forms the basis for Diffie-Hellman key exchange, because modular exponentiation can be efficiently computed, but no known way exists to efficiently compute the reverse function.
Turing machine decider by Ciro Santilli 37 Updated +Created
A Turing machine decider is a program that decides if one or more Turing machines halts of not.
Of course, because what we know about the halting problem, there cannot exist a single decider that decides all Turing machines.
E.g. The Busy Beaver Challenge has a set of deciders clearly published, which decide a large part of BB(5). Their proposed deciders are listed at: discuss.bbchallenge.org/c/deciders/5 and actually applied ones at: bbchallenge.org.
But there are deciders that can decide large classes of turing machines.
Many (all/most?) deciders are based on simulation of machines with arbitrary cutoff hyperparameters, e.g. the cutoff space/time of a Turing machine cycler decider.
The simplest and most obvious example is the Turing machine cycler decider
Superconducting magnet vendor by Ciro Santilli 37 Updated +Created
Once that example is clear, we see that the exact same separation of variables can be done to the Schrödinger equation. If we name the constant of the separation of variables for energy, we get:
Because the time part of the equation is always the same and always trivial to solve, all we have to do to actually solve the Schrodinger equation is to solve the time independent one, and then we can construct the full solution trivially.
Once we've solved the time-independent part for each possible , we can construct a solution exactly as we did in heat equation solution with Fourier series: we make a weighted sum over all possible to match the initial condition, which is analogous to the Fourier series in the case of the heat equation to reach a final full solution:
The fact that this approximation of the initial condition is always possible from is mathematically proven by some version of the spectral theorem based on the fact that The Schrodinger equation Hamiltonian has to be Hermitian and therefore behaves nicely.
It is interesting to note that solving the time-independent Schrodinger equation can also be seen exactly as an eigenvalue equation where:
The only difference from usual matrix eigenvectors is that we are now dealing with an infinite dimensional vector space.
Furthermore:
Neil Fernandez by Ciro Santilli 37 Updated +Created
“Especially my father. He was doing most of it and he is a savoury, strong character. He has strong beliefs about the world and in himself, and he was helping me a lot, even when I was at university as an undergraduate.”
An only child, Arran was born in 1995 in Glasgow, where his parents were studying at the time. His father has Spanish lineage, having a great grandfather who was a sailor who moved from Spain to St Vincent in the Carribean. A son later left the islands for the UK where he married an English woman. Arran’s mother is Norwegian.
“My father was writing and my mother is an economist. They both worked from home which also made things easier,” Arran says.
A bit like what Ciro Santilli feels about himself!
One of the articles says his father has a PhD. TODO where did he work? What's his PhD on? Photo: www.topfoto.co.uk/asset/1357880/
www.thetimes.co.uk/article/the-everyday-genius-pxsq5c50kt9:
Neil, a political economist, attended state and private schools in Hampshire but was also taught for a period at home by his mother.
It’s strange because for most people maths is a real turn-off, yet maths is all about patterns and children of two or three love patterns. It just shows that schools are doing something seriously wrong.”
Step busy beaver by Ciro Santilli 37 Updated +Created
The step busy beaver is a variant of the busy beaver game counts the number of steps before halt, instead of the number of 1's written to the tape.
As of 2023, it appears that BB(5) the same machine, , will win both for 5 states. But this is not always necessarily the case.
Key exchange by Ciro Santilli 37 Updated +Created

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