Corpus evidence — top 10 passages

Most-relevant passages from the entire indexed corpus (67,286 paragraph chunks across YouTube transcripts, PubMed, arXiv, archive.org, Stanford Encyclopedia of Philosophy, OpenAlex, and more) ranked by semantic similarity (bge-small-en-v1.5).

1. 01 · _intake0.948

   > electrons never changes according to the shinger equation if you just do particle quantum mechanics you're going to be stuck with the same number of particles that you always had you need to sort of

   _intake/claims-allbranch/curated-low/quantum-mech/002-electrons-never-changes-according-to-the-shinger-equation-if.md

2. 02 · _intake0.786

   - [`001-but-since-then-we-have-relativity-and-quantum-mechanics-and-`](quantum-mech/001-but-since-then-we-have-relativity-and-quantum-mechanics-and-.md) — score=8 `00:13:57.910` — But since then we have relativity and quantum mechanics And so forth so we have a better idea now of what the law is Fun - [`002-electrons-never-changes-according-to-the-shinger-equation-if`](quantum-mech/002-electrons-never-changes-according-to-the-shinger-equation-if.md) — score=8 `00:36:54.400` — electrons never changes according to the shinger equation if you just do particle quantum mechanics you're going to be …

   _intake/claims-allbranch/curated-low/INDEX.md

3. 03 · _intake0.786

   - [`001-but-since-then-we-have-relativity-and-quantum-mechanics-and-`](quantum-mech/001-but-since-then-we-have-relativity-and-quantum-mechanics-and-.md) — score=8 `00:13:57.910` — But since then we have relativity and quantum mechanics And so forth so we have a better idea now of what the law is Fun - [`002-electrons-never-changes-according-to-the-shinger-equation-if`](quantum-mech/002-electrons-never-changes-according-to-the-shinger-equation-if.md) — score=8 `00:36:54.400` — electrons never changes according to the shinger equation if you just do particle quantum mechanics you're going to be …

   _intake/claims-allbranch/curated/INDEX.md

4. 04 · yt0.780

   Random functions you picked in some potential will in fact evolve with time in such a way that measurable quantities will change with time. The odds for x or the odds for p, odds for everything else, will change with time, okay? So stationary states are very privileged, because if you start them that way, they stay that way, and that's why when you look at atoms, they typically stay that way. But once in a while, an atom will jump from one stationary state to another one, and you can say that looks like a contradiction. If it's stationary, what's it doing jumping from here to there? You know t…

   yt/Iy6RspNw80E-24-quantum-mechanics-vi-time-dependent-schr-dinger-equation/transcript.txt

5. 05 · yt0.773

   I hope all of you know that this e^(i)^( )absolute value squared is 1. So it does not depend on time. Even though Y depends on time, Y *Y has no time dependence. That means the probability for finding that particle will not change with time. That means if you start the particle in the ground state, Y, and let's say Y^(2) in fact looks pretty much the same, it's a real function, this probability does not change with time. That means you can make a measurement any time you want for position, and the odds don't change with time. It's very interesting. It depends on time and it doesn't depend on t…

   yt/Iy6RspNw80E-24-quantum-mechanics-vi-time-dependent-schr-dinger-equation/transcript.txt

6. 06 · yt0.768

   They said there's aspects of light, which is supposed to be a wave, which are particle-like. Einstein said that. There are aspects of particles like electrons that are wave-like. Louis de Broglie, following work by Niels Bohr and others, said that. And this whole thing coalesces almost exactly a hundred years ago in 1925 in the theory of quantum mechanics. And almost right at the same time, two different versions of it came out. Werner Heisenberg had his version called matrix mechanics. Erwin Schrodinger had his version called wave mechanics. They show that they were actually mathematically eq…

   yt/_TBNJyztai0-sean-carroll-explains-the-biggest-ideas-in-the-universe-full/transcript.txt

7. 07 · yt0.757

   Maybe the equation says that if you start with an electron wave all spread out, it will sort of localize itself near some point and it will look like a particle. It turns out not to be true. The equations don't care about your feelings. It's the opposite. If you start out with a localized electron wave, it will spread out all over the place. So it was yet another physicist, Max Born, different than Niels Bohr, who pointed out the right way to think about Schrodinger's wave function. He said think about what happens when you measure a property of the electron, like its position, or its velocity…

   yt/_TBNJyztai0-sean-carroll-explains-the-biggest-ideas-in-the-universe-full/transcript.txt

8. 08 · yt0.757

   So if you like, you can draw a little cloud whose thickness, if you like, measures the probability for finding it at that location. So that will have all kinds of shape. It looks like dumbbells, pointing to the north pole, south pole, maybe uniformly spherical distribution. They're all the probability of finding the electron in that state, and it doesn't change with time. So a hydrogen atom, when you leave it alone, will be in one of these allowed states. You don't need the hydrogen atom; this particle in a box is a good enough quantum system. If you start it like that, it will stay like that;…

   yt/Iy6RspNw80E-24-quantum-mechanics-vi-time-dependent-schr-dinger-equation/transcript.txt

9. 09 · wikisource0.755

   (at the coordinate origin!) is not always zero. Aren't electrons and protons more "penetrable" than molecules? The situation becomes even clearer if we apply Ehrenfest's considerations to the case of two molecules with different masses. The general solution of Schrödinger's equation is then

   wikisource/note-on-quantum-statistics/page.txt

10. 10 · yt0.753

    Many physicists would say, "No, it does." So the statement is that the electron explores both routes at the same time at once, let's say, on its root from the electron gun through the slits to the screen. So that's a very strange picture of reality. We surely think of particles as following definite paths, and it might be that you don't know quite which path it's gonna take, but surely you would say it, in reality, it will go one route or the other route. But that experiment, which I emphasize has been done now many times, tells us that nature is not like that. It tells us that the electron mu…

    yt/BHEhxPuMmQI-physicist-brian-cox-explains-quantum-physics-in-22-minutes/transcript.txt