The hydrogen atom ground state

[@paulbk2322]

One of those safest places in KZbin where I can press the like button and praise the video first and then relax back to watch the video......thank you very much Prof. M team👍👍👍👍

[@ProfessorMdoesScience]

Thanks for your kind words! :)

[@itsawonderfullife4802]

Your high quality QM videos are greatly appreciated. Thanks. Anxiously waiting for more in other topics.

[@ProfessorMdoesScience]

Glad you like them! :)

[@YossiSirote]

Excellent explanation of p(r) vs R(r)! I really appreciated your geometric insight. 😊

[@ProfessorMdoesScience]

Glad it was helpful!

[@YossiSirote]

At 20:15 you ask: “what is the mean of this?” I thought you meant what is the mean value of the electron distance , which is actually 1.5a_0. But in the captions you said “meaning”. 😂 … Either way - great video.

[@ProfessorMdoesScience]

Ups! (blush)

[@greenstar9385]

Those videos are beyond excellent, do you mind sharing your future projects on the channel or maybe present a map of the several components of QM, then say what we've covered so far and where we are heading to

[@ProfessorMdoesScience]

Great suggestion! We're actually working on a website to go along with the channel that will include what you are asking for as well as other material such as problems+solutions :)

[@sandippaul468]

Ma'am can you please start a full course on Quantum Optics? That will be very helpful. And we missed you two.

[@ProfessorMdoesScience]

Thanks for the suggestion! We are hoping to finish the basics of quantum mechanics first, but certainly want to extend our topics and quantum optics is one of them!

[@quantum4everyone]

Thanks for another very nice video. I have just two comments. The first one is relatively minor. When mentioning the virial theorem, you might also want to include the much more general Kramers-Pasternak relations, which give closed-form solutions for the expectation values for any power of r (positive or negative) in any energy eigenstate. Very powerful, but not very well known. The second comment is more substantial. When discussing the maximal probability for the electron in the ground state, you need to discuss two different cases. One is looking at the probability to be in a thin spherical shell, while the other is simply the probability to be in an infinitesimal cube. You do properly describe the former, which shows that the location where the maximum occurs is at the Bohr radius for the ground state. You also describe properly why the probability goes to zero at the origin, namely that the volume of the thin shell shrinks to zero as r goes to zero. But, if you instead look at the probability to be in an infinitesimal cube, the probability is maximal at the origin, indicating for s-wave states, one can think of them as being most likely inside the nucleus. This is not a crazy thing to think of, as the phenomenon of electron capture occurs precisely because s-wave electrons have a nonzero probability to be inside the nucleus. The main reason why the electron is not found inside of the nucleus “most of the time,’ even if it is most probable to (in the cubic volume case), is because the size of the nucleus is so small.

[@ProfessorMdoesScience]

Thanks for the comment! We focused on the virial theorem to relate it to a recent video in which we cover it, but thanks for raising the Kramers-Pasternak relations, may be interesting to look at them in the future. Regarding the discussion of the probability in a spherical shell, that is down to a practical choice: the video is already too long as it is, and we had to choose what to focus on. As we've been using the ionisation energy and Bohr radius throughout our discussion of hydrogen, we decided to focus on these two quantities in this video to provide some more context as to their meaning. We are actually preparing problems to go with the videos, and the study of the probability in a cube is something we explore in one of these problems :)

[@ProfessorMdoesScience]

And I just found your preprint on it, thanks for pointing it out! :)

[@quantum4everyone]

I assume you mean the work we did on Kramers-Pasternak relations. Yes, that has been published in European Journal of Physics. Key to that is that one can get the inverse second moment without using the Feynman-Hellman theorem, but instead via operator algebra. This is because of my focus on working on quantum mechanics without using calculus. Glad to hear that you plan on discussing the probability distributions in small codes. This is usually not discussed in textbooks, but is important.

[@ProfessorMdoesScience]

@@quantum4everyone We're reading the paper with interest, thanks! :)

[@photon7777777]

Excellent, really clear, thanks :)

[@ProfessorMdoesScience]

Glad it helped!

[@hugom6388]

Would it be correct that at higher energy levels the kinetic energy of the electron decreases as potential energy increases?

[@ProfessorMdoesScience]

The kinetic energy is associated with the curvature of the wave function. You can qualitatively understand this by considering that, in the position representation, the kinetic energy operator is the second derivative with respect to position. In this context, the more "wiggly" the wave function, the higher the kinetic energy. If you look at the higher excited states of hydrogen, you will see that they do become increasingly "wiggly" (the number of nodes increases, and therefore so does the curvature). As a result, the kinetic energy grows with the excited state. I hope this helps!

[@snjy1619]

❤❤❤

[@StephenGillie]

It's so weird hearing "so-called" in a neutral way, when it was originally an insult. But I guess KZbin has reclaimed it.

[@ProfessorMdoesScience]

Quite commonly used in our area too :)

[@Handelsbilanzdefizit]

Replace electron with anti-proton! Would this work? Now you studied hydrogen well enough, make suggestions about fusion. Some of the first quant.-physicists had enormous pressure to deliver something practical (A-Bomb). Funding, personal career, etc. ... depended on results. Think, climate doesn't create enough urgence to todays scientists.

[@ProfessorMdoesScience]

One can definitely study other hydrogen-like systems with these equations by replacing the proton or electron by other analogous particles (e.g. positron, muon, etc). However, for the study of fusion one would need to go beyond the electrostatic interaction we are considering here. And one of us does actually use quantum mechanics to discover new materials that could help address environmental sustainability :)

[@haniamritdas4725]

We can learn so much from statistics. But these single points on a root mean square distribution normalised over an infinite domain are nothing but statistical necessities. They give us information about the world, but they are not a theory of motion or composition; just generalized quadratics from abstract number theory. These days the scientists are claiming that our statistical analysis proves that reality is merely a statistical composition, but this is a tautology at best, and a metaphysical foundation at worst. There are lies, damnable lies, and statistics. Then there's quantum mechanics.

[@angelmendez-rivera351]

This is one huge strawman. The vast majority of scientists do not claim that the universe is merely a statistical composition.

[@haniamritdas4725]

@@angelmendez-rivera351 The claims of the vast majority of scientists are not my concern. It is the tools and methods I am addressing, not the society. And my claim is not that the universe is anything at all, but simply and very narrowly this: the standard model of physics is not a physical theory, because it makes no testable claims. It is a device constructed for the statistical analysis of singly measured data points with linear algebra and harmonic analysis. The goal appears to have been to gather enough data points to plot a curve; but there was no theory of motion to emerge from these statistics to date. The only curve it produces is the standard deviation, because that is the output of a statistical device which runs data through the quadratic formulation of the wave function. You seem to want to make the issue personal; I have not identified any men at all, neither straw nor steel. I am only talking about theories and mathematics, not a society. Who cares if all the scientists in the world agree on their own best friends interests? But that has very little to do with advancing knowledge, much less getting the vehicle of empirical falsifiability out of the mud, where it stuck up to the axles since 1930. Everyone in the world believing that the quantum world is "itself" strangely statistical demonstrates that only that statistics makes no falsifiable claims. The earth itself has a 90% probabilistic valence around the Sun. If we tried to use the wave equation to determine its position and momentum, we would still have the same problem as The Standard Model: the uncertainty "principle" arises at all scales of measure from the application of the harmonic analysis; time and frequency domain tradeoffs are mathematical, not physical in their nature. But no one can falsify the claim that all data are statistical, and leap to the spurious conclusion that quantum interactions and motions can only be statistical. We wouldn't get any orbits at all from wave mechanics measuring planets by sight; not even Ptolemy's convoluted epicyclic. Certainly not ellipses. The planets would appear at points that had a regularity resembling the standard deviation from conforming to a statical envelope of distances and angles. I am sure that I could have misunderstood something in the maths. But I think that is true of the men in the room at Copenhagen too. Not to mention the world of mystical hippies their irrefutable assertions have produced. Speaking as one of the hippies.

[@haniamritdas4725]

I refer to the dogma that an electron's position or moment is nothing other than a statistical smear of probabilities until its probabilistic statistical value is "collapsed by the measurement of the wave function." This is what I would call "taking another statistical sample datum".

[@haniamritdas4725]

But as far as pure maths are concerned, the standard model is very beautiful construction that itself established a bridge between infinitesimal analysis and the Hermite algebra with a nifty constructor for linear algebraic convolutions of solutions. It's a beautiful thing indeed. But it isn't a physical theory or even a basis for a theory of anything but abstract quantification and algebraic manipulation. It makes no claims.

[@angelmendez-rivera351]

*The claims of the vast majority of scientists are not my concern.* You said, and I quote: "These days, the scientists are claiming that our statistical analysis proves that reality is merely a statistical composition..." So yes, you are concerned with such claims. And I am telling that no one actually makes this claim that you said scientists make. *It is the tools and methods I am addressing, not the society.* No, you are not addressing any methods or tools in your comment. You have named exactly 0 tools in your comment. *And my claim is not that the universe is anything at all, but simply and very narrowly this: the standard model of physics is not a physical theory, because it makes no testable claims.* This is false. The standard model makes many testable claims. Experimental data agrees with those claims to a very high degree of accuracy. *It is a device constructed for the statistical analysis of singly measured data points with linear algebra and harmonic analysis.* There is not a single experiment out there which is a reliant on a single data points, so this is a lie. *The goal appears to have been to gather enough data points to plot a curve; but there was no theory of motion to emerge from these statistics to date.* No, scientific theories do not come equipped with goals. Scientific theories are predictive mathematical frameworks that we can compare to experimental data. That is all we are dealing with. *The only curve it produces is the standard deviation, because that is the output of a statistical device which runs data through the quadratic formulation of the wave function.* Standard deviation is not a curve. Standard deviation is a fixed numerical quantity. I know you are trying to pretend that you understand basic statistical concepts, but throwing word salad around without knowing the terminology is not going to help you here. *You seem to want to make the issue personal; I have not identified any men at all, neither straw nor steel.* Yes, you did, and I already quoted you on it. You are being dishonest. *I am only talking about theories and mathematics, not a society.* Again, I quoted you. Lying is not going to get you anywhere. *Who cares if all the scientists in the world agree on their own best friends interests?* That is not how the scientific community works at all. The scientific community is one of competition. The incentive of a scientist is to prove that the other scientists are wrong. Everyone proposes a hypothesis, and everyone else test the hypothesis, then we all talk about the data, and we all try to refute each other. Whatever little survives that war of titans, whatever we find ourselves being unable to refute no matter how hard anyone tries, we isolate that, and we study it further. We use it as the base point for more testable predictions, further experimentation and observation, and we use as the basis for coming up with computer simulations and mathematical frameworks. Then, we repeat the process all over again. This is happening continuously, and the result is an ever self-refining stream of knowledge about the reality being studied. It leads to increasingly more accurate and precise descriptions of the phenomena being studied. This is the scientific method. This is how we created the Internet, and allowed you to post silly stuff like the science-denial that you are posting. This is how we brought to you medicine. This is how we brought to you refrigeration for food. *But that has very little to do with advancing knowledge, much less getting the vehicle of empirical falsifiability out of the mud, where it stuck up to the axles since 1930.* Citation needed. *Everyone in the world believing that the quantum world is "itself" strangely statistical demonstrates that only that statistics makes no falsifiable claims.* Yeah, except not everyone in the world believes that. So,... moot point. *The earth itself has a 90% probabilistic valence around the Sun.* Ah, here we go with the pseudo-science and the meaningless word salad and techno-babble. *If we tried to use the wave equation to determine its position and momentum, we would still have the same problem as The Standard Model: the uncertainty "principle" arises at all scales of measure from the application of the harmonic analysis;...* Yes, but the actual instrumental imprecision of the measurements would far exceed the uncertainty conferred by the uncertainty principle. Thus, this is irrelevant. No one would ever be able to measure the position of the Sun with a precision down to the micrometer. *time and frequency domain tradeoffs are mathematical, not physical in their nature.* Yeah, and? No physicist out there is claiming otherwise. *But no one can falsify the claim that all data are statistical, and leap to the spurious conclusion that quantum interactions and motions can only be statistical.* No one has claimed that quantum phenomena is "only statistical" and nothing else. *I am sure that I could have misunderstood something in the maths.* Oh, you _definitely_ have misunderstood many things here, but you already have demonstrated that you lack the intellectual honesty to be able to change your mind. So, you acknowledging that you may have misunderstood the maths ultimately does not earn you any points. *But I think that is true of the men in the room at Copenhagen too.* Yes, of course you believe that. This is typical. There are so many laypeople who barely know their multiplication tables and who have no physics education whatsoever, telling world-class experts in physics that they are wrong about everything that there is to know about physics, all without presenting even a shred of evidence to show for it. You are one of those. And you are the same kind of people who, after saying something so utterly dishonest and insidious, will turn around and say "I love science" as if you actually meant it. Yeah, sorry, but as far as I am concerned, you are no different than a flat Earther. You did not come here to ask questions about quantum mechanics. You came here to be an arrogant troll and insult scientists. I will not read your other replies to me, because it is now clear to me that interacting with you is an irredeemable waste of anyone's time.