You two have been instrumental in my self study of quantum mechanics. I really love the quantum world, and am inspired to utilize it's strange properties to solve nano-engineering problems. Thanks to you guys, and lots of hard work. I was allowed to skip semester 1 of undergraduate quantum mechanics and am heading into second semester QM even though I'm still a sophomore. Now I'm on track to finish graduate quantum field theory before I begin my senior thesis. I'm so excited! Can't wait to see more from you. You enable driven and self-directed learners like me to control their own destiny, unbeholden to the cage of bureaucracy
Thanks for your support! We've been very busy preparing the new academic year at Cambridge, so haven't been able to upload as often as we'd like. We are currently working on the next two videos on hydrogen, which will hopefully come out soon :)
@@ProfessorMdoesScience That's great! Thank you your content there are not many resources where we can learn from who can't afford a good education. I am an independent Quantum Computer Scientist and I have learnt everything from RUclips and Books. Please provide content whenever you feel like but don't stop. You guys don't understand how much it helps me and others.
When I first watched a video on this channel, I was having classes of quantum mechanics. Now I already got my degree in physics and I'm studying particle physics. Actually, while I'm watching this video about a particle formed by a proton and an electron, my last class was about electron-proton scattering.
I recognize the material in QM class so for this one i just have few questions: we can derive that the hydrogen ground state is spherically symmetric, but the illustration of the first excited state looks as if there are "bulges" of large probability pointing at +-z/x/y. 1. in the 1st excited state, will the electron charge density no longer be spherical (possible electric dipole moment)? 2. because l=1, can we define a magnetic dipole moment? 3. If we can, will the direction of magnetic dipole moment coincide with the bulges? maybe this deviates from the course structure, but thanks!
In general we can have electric and magnetic dipole moments for non-spherical eigenstates. For example, the expectation value of the magnetic dipole moment in an eigenstate |n,k,m_l> is given by -muB*sqrt(l*(l+1)), where muB is the so-called Bohr magneton. For the direction, you can also ask, for example, about the z component of the magnetic dipole moment, whose expectation value is -muB*m_l. I hope this helps!
Great point! It is actually instructive to write down the general solution (we hope to do that in some future video). In general, you can write the full general wave function in terms of generalized Laguerre polynomials. I hope this helps!
Love all your guys's videos. I'm curious: what's the point of going through k to calculate the wavefunction? Could we not keep everything in terms of n? Does using k make the calculation easier? Thanks!
When considering the general properties of central potentials, we introduce the quantum number "k" to label the distinct energy eigenvalues for a given set of orbital angular momentum quantum number (l,m_l). For a general central potential, the different energy eigenvalues can be labelled by E_{kl}. From this point of view, k is the most fundamental quantity. We discuss these points in this video: ruclips.net/video/MsZP7yxpeFg/видео.html However, when solving the radial equation for the specific case of the hydrogen atom, we find that the energy eigenvalues do not depend on k and l, separately, but only on their combination k+l. This is where we introduce this "derived" quantum number "n". You can equivalently work in terms of (k,l,m_l) or (n,l,m_l), remembering that n=k+l, and as long as you are consistent everything should work out. I hope this helps!
Would you guys ever consider making a video on (semi classical and quantum) Rabi oscillations in two state systems? It's a very interesting topic and would love to hear your take on it as you always seem to make difficult systems mathemtically system!
Thanks for the suggestion! Our plan is to explore 2-level systems after we finish with hydrogen, first with a focus on spin 1/2 systems, but then also more general 2-level systems. So we will hopefully cover this relatively soon!
Do you have plans to start relativistic quantum mechanics? I would love a review of special relativity then a series on relativistic quantum mechanics and feynman's path integral approach! That would be wonderful
Thanks for the suggestion! We do hope to first make some progress on non-relativistic quantum mechanics, but we do eventually hope to move towards quantum field theory :)
the ground state is a simultaneous eigenstate of Lx, Ly, Lz, but with eigenvalue 0. Note that is the maximum angular uncertainty, as all directions are equivalent.
The key point is that the expansion series must be finite to get physically valid solutions. This arises from the (admittedly long) solution to the eigenvalue equation for the hydrogen atom using a series expansion. We go in detail over this in the following video: ruclips.net/video/8NJm4Jkp0jY/видео.html I hope this helps!
How is artificial intelligence being used currently to calculate the eigenvalues and eigenfunctions of the 14 Lanthanides chemical elements of the periodic table?
Thanks for the suggestion! We are planning a full video series on spin, but in the meantime I'd encourage you to check out the videos on general angular momentum here: ruclips.net/p/PL8W2boV7eVfmm5SZRjbhOKNziRXy6yIvI Spin is simply a concrete example of this. I hope this helps!
@@ProfessorMdoesScience Bohm's Approach and Individuality, 2016, Oxford University Press: Basil J. Hiley: "There we see that if one of the particles enters the field of a Stern-Gerlach magnet, it is then deflected either "up" or "down" depending on the positions of each particle at the time just before the particle enters the magnetic field. The particle in this field has its trajectory changed, while the other particle continues in a straight line. At the same time both spin components become well defined. This is a surprising result, but clearly shows that the individual parts cannot be thought of as isolated "little spinning spheres," a point that was emphasized by Weyl (1931)."
Quantum professor Basil J. Hiley, 2016: "Quantum Trajectories: Dirac, Moyal and Bohm": "In many ways it seemed to be a new form of inner energy possessed by the particle, organising the flow lines in a novel way and suggesting a 'formative' cause rather than the traditional efficient cause. ....quantum phenomena emerged from a non-commutative phase space."
Yes! We do use these videos for our teaching. For example, starting a Master's level course next week on tight-binding theory where we use the videos on identical particles and second quantization :)
@@ProfessorMdoesScience If you could, posting links to practice problems and similar resources that your students go through would be really helpful. QM is a broad topic and is approached from many angles, having a single source for lecture followed by practice is super handy
@@dutonic Thanks for the suggestion! We have been working on preparing extra material (like problems+solutions) to go with the videos. Unfortunately, we are currently very busy and it is taking longer than we would like to prepare...
Is anyone familiar with the variation shown in the video linked below? I have been obsessed with it after first observing it back when I was in high school. I think it qualifies as a variation of Euler’s contain column studies The video and white paper describes the mechanical properties related this unique variation of Euler’s Contain Column studies. It shows how materials (representing fields) naturally respond to induced stresses in a “quantized“ manor. This process, unlike harmonic oscillators can lead to formation of stable structures. The quantized responses closely models various energy levels of the quantum wave function. The effect has been used to make light weight structures and shock mitigating/recoiled reduction systems. The model requires an exponential load increase and the collapse of resistance during transition, leading to the very fast jump to the next energy levels. ruclips.net/video/wrBsqiE0vG4/видео.htmlsi=waT8lY2iX-wJdjO3
![Seungmin "그렇게, 천천히, 우리(As we are)" | [Stray Kids : SKZ-PLAYER]](http://i.ytimg.com/vi/kAzmhLHePqU/mqdefault.jpg)
You two have been instrumental in my self study of quantum mechanics. I really love the quantum world, and am inspired to utilize it's strange properties to solve nano-engineering problems. Thanks to you guys, and lots of hard work. I was allowed to skip semester 1 of undergraduate quantum mechanics and am heading into second semester QM even though I'm still a sophomore. Now I'm on track to finish graduate quantum field theory before I begin my senior thesis. I'm so excited! Can't wait to see more from you. You enable driven and self-directed learners like me to control their own destiny, unbeholden to the cage of bureaucracy
This is great to hear, and good luck with your studies! :)
Why were you guys not uploading for past weeks. We love your content please upload more. Thank you for your content ❤️
Thanks for your support! We've been very busy preparing the new academic year at Cambridge, so haven't been able to upload as often as we'd like. We are currently working on the next two videos on hydrogen, which will hopefully come out soon :)
@@ProfessorMdoesScience That's great! Thank you your content there are not many resources where we can learn from who can't afford a good education.
I am an independent Quantum Computer Scientist and I have learnt everything from RUclips and Books. Please provide content whenever you feel like but don't stop.
You guys don't understand how much it helps me and others.
@@UsamaThakurr that is true 🤠
When I first watched a video on this channel, I was having classes of quantum mechanics. Now I already got my degree in physics and I'm studying particle physics. Actually, while I'm watching this video about a particle formed by a proton and an electron, my last class was about electron-proton scattering.
Good timing! :)
I have midterms next week, video just in time! Thank You!
Good timing :) And good luck with the midterms! Where are you studying?
@@ProfessorMdoesScience thanks! KAIST
I recognize the material in QM class so for this one i just have few questions: we can derive that the hydrogen ground state is spherically symmetric, but the illustration of the first excited state looks as if there are "bulges" of large probability pointing at +-z/x/y.
1. in the 1st excited state, will the electron charge density no longer be spherical (possible electric dipole moment)?
2. because l=1, can we define a magnetic dipole moment?
3. If we can, will the direction of magnetic dipole moment coincide with the bulges?
maybe this deviates from the course structure, but thanks!
In general we can have electric and magnetic dipole moments for non-spherical eigenstates. For example, the expectation value of the magnetic dipole moment in an eigenstate |n,k,m_l> is given by -muB*sqrt(l*(l+1)), where muB is the so-called Bohr magneton. For the direction, you can also ask, for example, about the z component of the magnetic dipole moment, whose expectation value is -muB*m_l. I hope this helps!
Is it instructive to try and normalise a general radial wavefunction, or better to just solve for specific examples when you need them?
Great point! It is actually instructive to write down the general solution (we hope to do that in some future video). In general, you can write the full general wave function in terms of generalized Laguerre polynomials. I hope this helps!
@@ProfessorMdoesScience Yeh that video would be really useful!
Excellent job explaining this 👏
Glad to hear! :)
I've subscribed. Thanks for your work.
Thanks! :)
Love all your guys's videos. I'm curious: what's the point of going through k to calculate the wavefunction? Could we not keep everything in terms of n? Does using k make the calculation easier?
Thanks!
When considering the general properties of central potentials, we introduce the quantum number "k" to label the distinct energy eigenvalues for a given set of orbital angular momentum quantum number (l,m_l). For a general central potential, the different energy eigenvalues can be labelled by E_{kl}. From this point of view, k is the most fundamental quantity. We discuss these points in this video:
ruclips.net/video/MsZP7yxpeFg/видео.html
However, when solving the radial equation for the specific case of the hydrogen atom, we find that the energy eigenvalues do not depend on k and l, separately, but only on their combination k+l. This is where we introduce this "derived" quantum number "n". You can equivalently work in terms of (k,l,m_l) or (n,l,m_l), remembering that n=k+l, and as long as you are consistent everything should work out. I hope this helps!
@@ProfessorMdoesScience Fantastic, thank you!
Would you guys ever consider making a video on (semi classical and quantum) Rabi oscillations in two state systems? It's a very interesting topic and would love to hear your take on it as you always seem to make difficult systems mathemtically system!
Thanks for the suggestion! Our plan is to explore 2-level systems after we finish with hydrogen, first with a focus on spin 1/2 systems, but then also more general 2-level systems. So we will hopefully cover this relatively soon!
@@ProfessorMdoesScience Wow, I can't wait!
Thank You ! you guys are godsend !!!
Thanks for watching! :)
Do you have plans to start relativistic quantum mechanics? I would love a review of special relativity then a series on relativistic quantum mechanics and feynman's path integral approach! That would be wonderful
Thanks for the suggestion! We do hope to first make some progress on non-relativistic quantum mechanics, but we do eventually hope to move towards quantum field theory :)
What L can also be the eigen operator for ground state 1S of hydrogen.atom
The ground state of the hydrogen atom corresponds to quantum number l=0 for the L^2 operator, and ml=0 for the Lz operator. I hope this helps!
the ground state is a simultaneous eigenstate of Lx, Ly, Lz, but with eigenvalue 0. Note that is the maximum angular uncertainty, as all directions are equivalent.
how will i know that what will be q for 3rd excited state it will be greater then k or less then if you could explain?
The key point is that the expansion series must be finite to get physically valid solutions. This arises from the (admittedly long) solution to the eigenvalue equation for the hydrogen atom using a series expansion. We go in detail over this in the following video:
ruclips.net/video/8NJm4Jkp0jY/видео.html
I hope this helps!
How is artificial intelligence being used currently to calculate the eigenvalues and eigenfunctions of the 14 Lanthanides chemical elements of the periodic table?
Hey could u plz make a video on spectrum of hydrogen atom in quantum mechanics
We are working on such a video at the moment, so it will appear in the near future :)
@@ProfessorMdoesScience will be waiting ma'am 🌸
make a playlist about quantum field theory
Thanks for the suggestion, we are hoping to get to more advanced topics once we've covered the basics of quantum theory :)
Can you do a vid on noncommutative spin? thanks
Thanks for the suggestion! We are planning a full video series on spin, but in the meantime I'd encourage you to check out the videos on general angular momentum here:
ruclips.net/p/PL8W2boV7eVfmm5SZRjbhOKNziRXy6yIvI
Spin is simply a concrete example of this. I hope this helps!
@@ProfessorMdoesScience Bohm's Approach and Individuality, 2016, Oxford University Press: Basil J. Hiley:
"There we see that if one of the particles enters the field of a Stern-Gerlach magnet, it is then deflected either "up" or "down" depending on the positions of each particle at the time just before the particle enters the magnetic field. The particle in this field has its trajectory changed, while the other particle continues in a straight line. At the same time both spin components become well defined. This is a surprising result, but clearly shows that the individual parts cannot be thought of as isolated "little spinning spheres," a point that was emphasized by Weyl (1931)."
Quantum professor Basil J. Hiley, 2016: "Quantum Trajectories: Dirac, Moyal and Bohm":
"In many ways it seemed to be a new form of inner energy possessed by the particle, organising the flow lines in a novel way and suggesting a 'formative' cause rather than the traditional efficient cause. ....quantum phenomena emerged from a non-commutative phase space."
can you plzz make a full playlist of hydrogen atom ?
We are working on it! We are currently preparing the next three videos, which should come out over the next few weeks...
Beautiful 😍❤️
mi avatar is what I did with mi eigen values. made a very nice structure with it. the form is just like corrugated carboard or roof trusses.
Looks nice!
just curious, do your cambridge students also watch these?
Yes! We do use these videos for our teaching. For example, starting a Master's level course next week on tight-binding theory where we use the videos on identical particles and second quantization :)
@@ProfessorMdoesScience If you could, posting links to practice problems and similar resources that your students go through would be really helpful. QM is a broad topic and is approached from many angles, having a single source for lecture followed by practice is super handy
@@dutonic Thanks for the suggestion! We have been working on preparing extra material (like problems+solutions) to go with the videos. Unfortunately, we are currently very busy and it is taking longer than we would like to prepare...
Is anyone familiar with the variation shown in the video linked below? I have been obsessed with it after first observing it back when I was in high school. I think it qualifies as a variation of Euler’s contain column studies
The video and white paper describes the mechanical properties related this unique variation of Euler’s Contain Column studies.
It shows how materials (representing fields) naturally respond to induced stresses in a “quantized“ manor.
This process, unlike harmonic oscillators can lead to formation of stable structures.
The quantized responses closely models various energy levels of the quantum wave function.
The effect has been used to make light weight structures and shock mitigating/recoiled reduction systems.
The model requires an exponential load increase and the collapse of resistance during transition, leading to the very fast jump to the next energy levels.
ruclips.net/video/wrBsqiE0vG4/видео.htmlsi=waT8lY2iX-wJdjO3
38:04
🥰🥰🥰