Nice I can't believe I have access to such great content free of cost Keep it up you guys!!

@ProfessorMdoesScience

2 жыл бұрын

Glad you like our videos! :)

Your approach toward many problems is so fundamental that it makes many things more apparent to me. I hope you keep making more content like this. Thank you for making free content.

@ProfessorMdoesScience

Жыл бұрын

Glad you like it, and we do think that going to fundamentals is important :)

You guys really should keep making these videos. This greatly accelerates education across the globe. Surprisingly I find them clearer than open course lectures and even some textbooks. There are a lot of editing decisions that I greatly appreciate and hope you guys can continue e.g: having a cheerful but not overly dramatic narrator to show their face at intro and outro; using electric chalkboard, accelerate the writing to save time, but don't slam the whole equation instantaneously so students feel more sense of continuity; writing out intermediate results that you are going to re-use, instead of just saying "please refer to equation 9.103"; keeping each derivation step "light", i.e. don't say things like "plug this and that it's clear that" and then show something that's totally recognizable from the previous step.

@ProfessorMdoesScience

Жыл бұрын

This is great to hear! We have been teaching for years and find all these points you highlight important for the learning process :)

Glad to have you back!

@ProfessorMdoesScience

2 жыл бұрын

Thanks! Glad to be back, and hopefully we'll manage to publish a little more regularly...

I have this super tough entrance exam coming, and I'm following you guys for the portion of Quantum Mechanics. I've studied quantum mechanics before but I've come across this level of detailed explanation and mathematical aid for the first time. Also, I'd love to contact you guys for something, it'd be really great if you could refer me on how to do so. Much Love and support from India. 🇮🇳 You guys are absolutely fantastic.

@ProfessorMdoesScience

2 жыл бұрын

Good luck with your exam, and glad that you find the videos helpful! Our contact details are in the "About" page of the channel, but let us know if you cannot find them.

They're back! Amazing!

@ProfessorMdoesScience

2 жыл бұрын

Thanks for watching! :)

Great video! Please do a video on Schrödinger vs. Heisenberg vs. Interaction picture

@ProfessorMdoesScience

2 жыл бұрын

Thanks for the suggestion, it is on our list! :)

@rodrigoappendino

2 жыл бұрын

I think I never heard about interaction picture. Good suggestion.

@ProfessorMdoesScience

2 жыл бұрын

The video on the Schrödinger vs. Heisenberg picture is now up: kzread.info/dash/bejne/ZHiBl6aMdNC2ZMY.html I hope you like it!

I found your videos after reading the book "The Making of the Atomic Bomb". Love the content.

@ProfessorMdoesScience

10 ай бұрын

Glad you like the videos!

Got an exam on this tomorrow. Watching this was a good study tool. Helped me understand it on a fundamental level

@ProfessorMdoesScience

Жыл бұрын

This is great to hear, good luck with the exam! Where are you studying?

Everytime I watch your videos, it is a new learning experience.....no apt words in my vocabulary to appreciate your wonderful efforts. Please make a detailed video on SPIN.

@ProfessorMdoesScience

Жыл бұрын

Thanks for your continued support :) And our next topic will indeed be spin!

@paulbk2322

Жыл бұрын

@@ProfessorMdoesScience Feeling excited!!!

Dude I almost lost my passion for physics after getting bogged down in exams instead of learning. You guys literally resurrected it 😅

@ProfessorMdoesScience

2 жыл бұрын

Great to hear! :) May I ask where you study?

For this video i only have a few, not very technical questions 1. Is there a way to tell if a problem has an analytic solution or not (from looking at the Hamiltonian?)? How do we know that such solution doesn't exist or that we just haven't found it? 2. Do you know what makes it necessary to use supercomputers to find solutions to Schrödinger equation instead of, say, my PC? What makes it so computationally demanding? 3. Do we know the different effects that might arise if the masses of the two charge particles are equal? Center of mass position expectation value should be in the middle, what about energy spectra? Can we still use quantum numbers n, l, and m? (I imagine this is the case of electron-positron binding before they eventually annihilate)

@ProfessorMdoesScience

2 жыл бұрын

Here are some thoughts: 1. It could certainly be the case that a problem has an analytical solution but that we haven't found it yet. In the context of atomic systems, molecular systems, and materials, one of the key problems making finding an analytical solution difficult arises from the electron-electron interaction. It is unknown how to treat such a two-body term analytically. 2. Yes! The way to numerically solve the eigenvalue equation of the Hamiltonian is usually to write the Hamiltonian in matrix form using a particular basis, and diagonalizing the matrix to find the eigenvalues and eigenstates. The basis used should in principle be infinite, and the numerical approximation comes by truncating this basis to make the calculations possible. Even with a basis truncation, we end up with a large basis (thousands/millions of basis states), which leads to very large matrices which are computationally expensive to diagonalize, hence the need for supercomputers. Bases that are commonly used include plane waves for materials (which are periodic) or localized states (e.g. atomic orbitals) for molecular systems. We hope to get to the study of condensed matter systems after we are done with our quantum mechanics series, so hopefully we'll explore some of these ideas then! 3. Very interesting question! We are planning a video where we explore this very point by looking at a few examples of "hydrogenic" systems (e.g. deuterium, tritium, positronium, muonium, ...). The solutions we'll find for the hydrogen atom will be in terms of the reduced mass, so we can then understand all these other systems by simply using the appropriate reduced mass. I hope this helps!

A very good presentation of the problem, also a very helpful and interesting channel, try to solve the problem of helium atom using approximation methods like perturbation and variational methods, it can be considered as an application of approximation methods and it helps to understand more the quantum behaviour of atoms.

@ProfessorMdoesScience

6 ай бұрын

Thanks for the suggestion! We are planning on starting a series on approximation methods and the helium atom would feature there! Hopefully we'll get to it soon :)

Shouldn't there be spin interaction terms? (like I asked in the Second Quantization Hamiltonian video) Or are these the Hyperfine structure terms you mentioned? Also if we can add spin interactions and relativistic terms simply to the Hamiltonian, does that mean we can always use the Schrödinger Equation with an appropriate Hamiltonian? I'd imagine that, since we have different order derivatives, this is not Lorentz Invariant?

@ProfessorMdoesScience

22 күн бұрын

Indeed the inclusion of spin will lead to the sort of terms you are discussing, and we will explore those in a later series :)

why do we use a electrostatic potential? the electron and the proton are moving right? maybe because these particles are quantum objects we should not try to imagine them as moving objects and we can use a electrostatic potential because of that?

@ProfessorMdoesScience

2 жыл бұрын

Interesting question! A full description of the quantum mechanics of microscopic systems requires quantum field theory (which incorporates Einstein's special theory of relativity). As such, and as hinted at in the video, the Hamiltonian we use (with the specific form of the kinetic energy and the electrostatic potential) is just a starting point. It nonetheless describes the major features of the hydrogen atom, so it is a worthwhile starting point.

Isn’t it easier to fix the proton as if it’s a static particle at the center of mass and now all the energy is carried by the electron. So because the COM is static the momenta for both particles should be the same. And then by expressing the momentum of the proton through the electron, we can reduce the problem of two particle to a single particle problem. Then the Hamiltonian is expressed in terms of electron momentum and reduced mass. Without considering the relative coordinates and momenta. Seems much easier than to deal with relative coordinates and momenta. Or am I missing something?

@ProfessorMdoesScience

Жыл бұрын

The problem is that fixing the proton in such a way is not physical. The center of mass of the electron-proton system is not at the proton, so fixing the proton means you are not in the center of mass coordinate system, but in some other coordinate system. And in this case, you cannot separate the degrees of freedom neatly, resulting in much more complex expressions. What you are suggesting would only work if the center of mass was truly located at the proton position, and this would only be true if the proton had infinite mass. While this is something that is sometimes done, it is an approximate solution only because the proton doesn't have infinite mass. I hope this helps!

Great video! Please keep going. Is there any sequence to watch these videos and get the best of it?

@ProfessorMdoesScience

2 жыл бұрын

Glad you like it! We are working on a website to help guide students through the videos (and also include problems+solutions). But in the meantime, a good strategy is to follow the various playlists, with a good order being: 1. The postulates, which provides the basic background: kzread.info/head/PL8W2boV7eVfmMcKF-ljTvAJQ2z-vILSxb 2. The quantum harmonic oscillator, which provides a nice example of applying the postulates: kzread.info/head/PL8W2boV7eVfmdWs3CsaGfoITHURXvHOGm 3. Angular momentum, which provides another nice (and useful) example of the postulates: kzread.info/head/PL8W2boV7eVfmm5SZRjbhOKNziRXy6yIvI 4. Central potentials (still ongoing, and forms the basis for the also ongoing hydrogen series): kzread.info/head/PL8W2boV7eVfkqnDmcAJTKwCQTsFQk1Air After those, there are more advanced topics like "identical particles" or "second quantization", but I would only recommend those after you've mastered those above. Overall, we are hoping that in the next year or so we'll have a complete course on the basics of quantum mechanics. I hope this helps!

@meerfaraaz6894

2 жыл бұрын

@@ProfessorMdoesScience Thank you so much! You guys are doing great job. These videos are like hidden treasure.

Thank you!

@ProfessorMdoesScience

2 жыл бұрын

Thanks for watching!

It's amazing that this still works, with the proton being composed of 3 smaller particles.

@ProfessorMdoesScience

Жыл бұрын

Similar ideas where we combine smaller components into "effective" larger scale views work in many areas of physics, not only here. A good example is thermodynamics :)

@StephenGillie

Жыл бұрын

@@ProfessorMdoesScience Does that mean the Strong Nuclear Force cancels out the uncertainty? Or just that nobody's done the math for quarks in a nucleus? Thanks for these great videos.

@ProfessorMdoesScience

Жыл бұрын

@@StephenGillie I think the computational cost of treating the quarks/gluons in the nucleus when describing hydrogen would be prohibitive. Phil Anderson wrote a very famous paper "More is different" that provides a nice perspective on questions of this nature: www.science.org/doi/10.1126/science.177.4047.393

@StephenGillie

Жыл бұрын

@@ProfessorMdoesScience Computational costs are always falling, so you're suggesting it's just a matter of time before we have enough neural and quantum compute power, and maybe new mathematical models, to better understand this situation. It's like back in the 1970s, when Doom was computationally prohibitive, and we had to make due with D&D. Thank you for the hope in the future.

Thanks for the Video

@ProfessorMdoesScience

Жыл бұрын

Thanks for watching!

Thank you

@ProfessorMdoesScience

Жыл бұрын

Thanks for watching!

1:27 Are kilograms the conventional unit of mass in this context? Personally I could get used to yoctograms.

@ProfessorMdoesScience

2 жыл бұрын

You are absolutely correct to note that kg are not ideal units for particles like electrons and protons. Here we use kilograms to give a sense of scale, but the usual units used to study atomic/molecular systems are so-called "atomic units" in which the unit of mass is the mass of the electron. Hope this helps!

You've got the mother quality and make this chore easier. Dan Blatecky USA

@ProfessorMdoesScience

20 күн бұрын

Thanks for your support!

Thanks!

@ProfessorMdoesScience

6 ай бұрын

Thanks for watching!

Fantastic presentatiom

@ProfessorMdoesScience

4 ай бұрын

Glad you like it!

One thing that is missing in the video is the explanation that the center of mass and relative coordinates and momentum behave like position-momentum operators. The transformation given in @10:02 is a quantum canonical transformation, this is, it preserves the canonical commutation relations , [R,P]=[r,p]=i h.

@ProfessorMdoesScience

2 жыл бұрын

You are absolutely correct. We do in fact cover this exact point in the video on two interacting quantum particles: kzread.info/dash/bejne/nYOp0qt-mLzKiZs.html Thanks for bringing this up!

@zray2937

2 жыл бұрын

@@ProfessorMdoesScience Excellent.

dear ma'am, how did you derive relative momentum expression as shown in the video?

@ProfessorMdoesScience

2 жыл бұрын

We go over the details of this in the video on two interacting quantum particles: kzread.info/dash/bejne/nYOp0qt-mLzKiZs.html More generally, the center of mass and relative coordinates are the same we would use in a classical 2-body system.

@sayanjitb

2 жыл бұрын

@@ProfessorMdoesScience Thanks a lot.

Why did we ignore the equation of motion for a free particle and solve only the equation of motion for the bound state? Shouldn't we solve both the equations and then multiply them to get the actual wave function?

@ProfessorMdoesScience

Жыл бұрын

You are correct that the energy eigenstates of the electron-proton system include bound (E0). Hydrogen being the name we give to the bound states of the electron-proton system makes it natural to focus on the bound states. We do hope to discuss unbound states in the future, and not only for hydrogen but for general potentials!

@ 12:48 A FREE PARTICLE IS A PARTICLE THAT IS MOVING ALONG A STRAIGHT LINE (if it is moving) AND WITH A CONSTANT VELOCITY (for instance, v = 0, stationary). @ 12:57 "Forget about it" means assuming its KE = 0 (and adding it to the other KE) and its wave function Ψ = 1 (and multiplying it with the other wave function). P.S. In this video and the next one nothing is said explicitly about the consequences for the relative momentum-operator!

@lepidoptera9337

21 күн бұрын

There is no velocity in quantum mechanics. The relevant conserved quantity is momentum.

@jacobvandijk6525

21 күн бұрын

@@lepidoptera9337 The fact that momentum is conserved does not mean there is no velocity. Without velocity there is no momentum.

@lepidoptera9337

21 күн бұрын

@@jacobvandijk6525 That is a misconception from classical mechanics (and a trivialization to boot, see the derivation of the rocket equation). In quantum mechanics we can measure momentum, but we can't measure velocity.

@jacobvandijk6525

21 күн бұрын

@@lepidoptera9337 Right, but I never said we can measury velocitiy ;-)

@lepidoptera9337

21 күн бұрын

@@jacobvandijk6525 If you talk about velocity, then you have to tell me how you can measure it. The simple fact is that you can't, so it's pointless to talk about it. Velocity is an emergent property for macroscopic systems. At most you don't understand how it emerges (from repeated weak measurements).

Here's what I don't understand- a Hydrogen atom in the smallest atom, correct? So why can it pass through, say, stainless steel, which is WAY more dense?

@ProfessorMdoesScience

Жыл бұрын

When you think about the density of a material (e.g. steel) you are describing how closely-packed the atoms are in that material. Even in very dense materials, there is a lot of "empty space" between atoms. When you then think about the hydrogen atom passing through steel, you are thinking about an individual (small) atom passing through the stainless steel material. Hydrogen is so small that it can relatively easily move inside materials, even if they are relatively dense, by "squeezing through" in between the atoms. This is a very simple picture, but I hope it helps you think about this!

So, there are no neutrons in the hydrogen atom?

@ProfessorMdoesScience

11 ай бұрын

Hydrogen has a single proton in the nucleus. You can find additional isotopes of hydrogen with neutrons in the nucleus, of which two are naturally occuring: deuterium with one proton and one neutron, and tritium with one proton and two neutrons. I hope this helps!

I FORGOT HOW TO GET ATOMIC WEIGHT OF A NEBULA FROM THIS UNIT

Why we consider hydrogen atom in three dimension

@ProfessorMdoesScience

Жыл бұрын

Space is 3-dimensional, so when we consider the physics of (quantum) particles we need to consider their motion in 3D. I hope this helps!

Hi ma'am

Prof. Mommy does the hydrogen atom

This field model may be related to the your topic. kzread.info/dash/bejne/qaZ21dOidZPcd5c.htmlsi=waT8lY2iX-wJdjO3 Thanks for your informative and well produced video. You and your viewers might find the quantum-like analog interesting and useful. I have been trying to describe the “U” shape wave that is produced in my amateur science mechanical model in the video link. I hear if you over-lap all the waves together using Fournier Transforms, it may make a “U” shape or square wave. Can this be correct representation Feynman Path Integrals? In the model, “U” shape waves are produced as the loading increases and just before the wave-like function shifts to the next higher energy level. Your viewers might be interested in seeing the load verse deflection graph in white paper found elsewhere on my KZread channel. Actually replicating it with a sheet of clear folder plastic and tape. Seeing it first hand is worth the effort.

hydrogen is not an atom it is the electron itself, this misunderstanding stems from the the false theory of water being H2O

@DrDeuteron

Ай бұрын

Bro. This is like the one dimension earth theory. It’s just flat, it’s a line.they are called lerfs.

What I never understood. Assuming you have a system with many solutions, eigenfunctions (Ψ_1 and Ψ_2). The probabilities of first solution sums up to '1' = ∫ dx Ψ_1* Ψ_1 The probabilities of second solution sums up to '1' = ∫ dx Ψ_2* Ψ_2 How can the combined solution of both (Ψ_1 + Ψ_2) also sum up to '1' ? Are these functions normalized by coefficients, like in a mixed-state (aΨ_1 + bΨ_2). So, that the total probability sums up to '1' Or is interference the answer, that we always get '1' at the end, regardless how many solutions we add. Sorry, for my bad english and naive question. I'm a layman working for german police. I just watch this video because of quarantine-boredom, caused by Corona. ^^

@zray2937

2 жыл бұрын

the coefficients of Ψ_t=aΨ_1 + bΨ_2 has to be such that Ψ_t is normalized ( ∫ dx Ψ_t* Ψ_t=1).