I joined this channel today because I was confused about the solutions of harmonic oscillator in 1-D and 3-D my professor told me that in one dimension we have to take either even or odd solutions of the power series but in 3D we have to take both because of degeneracy so I just randomly typed and I find this channel. So that's my story how I joined this quantum world
Hey, I recently stumbled across your account and I greatly appreciate the effort you put into explaining these complicated topics in a mathematical accurate but easy to follow manner. You are doing some great work here and it has helped me a lot getting more familliar with quantum mechanics and I am very thankful for that! I read in one of the other comments that you were planning on doing a series about perturbation theory and I wanted to express that I would love videos about this topic because I am currently learning the concept of the degenerate perturbation theory in my bachelor, but have encountered some stuff that I am not fully understanding yet. So I really hope that this series is still on your radar and will hopefully come soon :)
Perturbation theory is definitely a topic we'll cover. The plan is to cover it after spin 1/2 particles, which we are working on now, so hopefully soon!
Ooh i have some ideas for this: 1. In the 2nd excited state case (with R₂₀ and R₀₂) due to those still being degenerate, will linear combination of the two still result in 7/2h̅ω energy? funny that two radial probability of finding a particle can exist with no change in energy. maybe transition between R₂₀ and R₀₂ is possible without energy cost, like being in an equipotential surface 2. the energy eigenvalues are equally spaced and constant √h̅/mω appears like in the 1D case. this makes me think algebraic method with ladder operators is still possible even in the 3D case 3. Both coulomb potential (1/r²) and harmonic oscillator (r²) result in bounded energy eigenfunctions. This made me think that maybe there is a pattern in the shape of eigenfunctions compared the shape of potential (what kind of eigenfunction when we choose which power of r) 4. This being a harmonic oscillator potential, is it possible to build 3D coherent state? if 1D coherent state *looks* like its vibrating, maybe the 3D one actually look like its orbiting thanks!
Thanks for your suggestions, some thoughts: 1. They are indeed degenerate, and perhaps it looks strange as we are not so used to thinking in terms of orbital angular momentum. Perhaps an easier way to think about these states with 7/2*hbar*omega energy is to consider their form in the "Cartesian" form: ua-cam.com/video/K5YsxsHXGHc/v-deo.html 2. Absolutely, and this is again clearer in the "Cartesian" approach. 3. Good point, but note that the Coulomb potential results in both bounded and unbounded states, whereas the harmonic potential only in bounded states. 4. An interesting point worth exploring :) I hope this helps!
We try to make the lectures as self-contained as possible, but there are always some dependencies. If you check out the "Playlists" page of our channel, we group videos there in such a way that following a given playlist in order should be the most useful approach for learning. I hope this helps!
I've gone through postulates, angular momentum, and now quantum harmonic oscillator playlists. Great stuff. Is there an order you would recommend exploring future content in?
These culminate in the series on central potentials and the hydrogen atom (the latter under construction). This provides a nice overiew of single-particle quantum mechanics. Moving forward, it would make sense to start exploring quantum mechanics for multiple particles, for which we have these two playslists: ua-cam.com/play/PL8W2boV7eVfnJ6X1ifa_JuOZ-Nq1BjaWf.html ua-cam.com/play/PL8W2boV7eVfnSqy1fs3CCNALSvnDDd-tb.html We have quite a few other topics, but we don't have enough videos yet in many. For example, we have a short series on density operators, which will form the basis for a series on quantum statistical mechanics, but we are not there yet... I hope this helps!
For N=1, in another video it was stated that its 3 times degenerate when it was used in cartesian. yet here it seems singly degenerate. Can you explain this discrepancy?
The n=0 state (ground state) is single degenerate, but the n=1 state (first excited state) is triply degenerate. This is true here but also in Cartesian coordinates. In the Cartesian case, the three degenerate states correspond to the excitation being along x, or along y, or along z. I hope this helps!
A good starting point are the postulates of quantum mechanics by following this playlist: ua-cam.com/play/PL8W2boV7eVfmMcKF-ljTvAJQ2z-vILSxb.html And a good one following it are the videos on the quantum harmonic oscillator, which provide a concrete example of the basic theory behind the postulates: ua-cam.com/play/PL8W2boV7eVfmdWs3CsaGfoITHURXvHOGm.html I hope this helps!
Your videos are candy in my subscription inbox
This is great to hear! :)
The way you explain all these complicated stuff in a simple and straightforward manner is extremely impressive
Glad you like it!
God bless you and my dear friend idil who suggested me this video.
Glad you like the video!
I joined this channel today because I was confused about the solutions of harmonic oscillator in 1-D and 3-D my professor told me that in one dimension we have to take either even or odd solutions of the power series but in 3D we have to take both because of degeneracy so I just randomly typed and I find this channel. So that's my story how I joined this quantum world
Glad you found us! :)
Hey, I recently stumbled across your account and I greatly appreciate the effort you put into explaining these complicated topics in a mathematical accurate but easy to follow manner. You are doing some great work here and it has helped me a lot getting more familliar with quantum mechanics and I am very thankful for that!
I read in one of the other comments that you were planning on doing a series about perturbation theory and I wanted to express that I would love videos about this topic because I am currently learning the concept of the degenerate perturbation theory in my bachelor, but have encountered some stuff that I am not fully understanding yet. So I really hope that this series is still on your radar and will hopefully come soon :)
Perturbation theory is definitely a topic we'll cover. The plan is to cover it after spin 1/2 particles, which we are working on now, so hopefully soon!
Ah cool, new learning material for our preschool. 🤓
Good one! :)
This channel is amazing!
Glad you like it!
Nice to meet you again with another great video❤️
Glad to be back! :)
Ooh i have some ideas for this:
1. In the 2nd excited state case (with R₂₀ and R₀₂) due to those still being degenerate, will linear combination of the two still result in 7/2h̅ω energy? funny that two radial probability of finding a particle can exist with no change in energy. maybe transition between R₂₀ and R₀₂ is possible without energy cost, like being in an equipotential surface
2. the energy eigenvalues are equally spaced and constant √h̅/mω appears like in the 1D case. this makes me think algebraic method with ladder operators is still possible even in the 3D case
3. Both coulomb potential (1/r²) and harmonic oscillator (r²) result in bounded energy eigenfunctions. This made me think that maybe there is a pattern in the shape of eigenfunctions compared the shape of potential (what kind of eigenfunction when we choose which power of r)
4. This being a harmonic oscillator potential, is it possible to build 3D coherent state? if 1D coherent state *looks* like its vibrating, maybe the 3D one actually look like its orbiting
thanks!
Thanks for your suggestions, some thoughts:
1. They are indeed degenerate, and perhaps it looks strange as we are not so used to thinking in terms of orbital angular momentum. Perhaps an easier way to think about these states with 7/2*hbar*omega energy is to consider their form in the "Cartesian" form: ua-cam.com/video/K5YsxsHXGHc/v-deo.html
2. Absolutely, and this is again clearer in the "Cartesian" approach.
3. Good point, but note that the Coulomb potential results in both bounded and unbounded states, whereas the harmonic potential only in bounded states.
4. An interesting point worth exploring :)
I hope this helps!
Thank you so much for this explanation Professor M! ^.^
Thanks for watching! :)
Another upload. Great!
Thanks for watching! :)
Would you recommend an order to follow all the lectures or are they independent and can stand alone?
We try to make the lectures as self-contained as possible, but there are always some dependencies. If you check out the "Playlists" page of our channel, we group videos there in such a way that following a given playlist in order should be the most useful approach for learning. I hope this helps!
You forgot to consider the case, k=1 and l=0 for n=1.
k can only take even values, so for n=1 the only possibility is k=0 and l=1. I hope this helps!
Can you consider the coherent state of this 3-d harmonic oscillator?
Yes, it is possible to do that!
I've gone through postulates, angular momentum, and now quantum harmonic oscillator playlists. Great stuff. Is there an order you would recommend exploring future content in?
These culminate in the series on central potentials and the hydrogen atom (the latter under construction). This provides a nice overiew of single-particle quantum mechanics.
Moving forward, it would make sense to start exploring quantum mechanics for multiple particles, for which we have these two playslists:
ua-cam.com/play/PL8W2boV7eVfnJ6X1ifa_JuOZ-Nq1BjaWf.html
ua-cam.com/play/PL8W2boV7eVfnSqy1fs3CCNALSvnDDd-tb.html
We have quite a few other topics, but we don't have enough videos yet in many. For example, we have a short series on density operators, which will form the basis for a series on quantum statistical mechanics, but we are not there yet...
I hope this helps!
For N=1, in another video it was stated that its 3 times degenerate when it was used in cartesian. yet here it seems singly degenerate. Can you explain this discrepancy?
The n=0 state (ground state) is single degenerate, but the n=1 state (first excited state) is triply degenerate. This is true here but also in Cartesian coordinates. In the Cartesian case, the three degenerate states correspond to the excitation being along x, or along y, or along z. I hope this helps!
Can you relate the constant k to spin of the oscillator?
This model is spinless, but we are preparing a new series on spin angular momentum, so stay tuned! :)
💎💎💎💎💎
Which videos do you recommend to start with?
A good starting point are the postulates of quantum mechanics by following this playlist: ua-cam.com/play/PL8W2boV7eVfmMcKF-ljTvAJQ2z-vILSxb.html
And a good one following it are the videos on the quantum harmonic oscillator, which provide a concrete example of the basic theory behind the postulates: ua-cam.com/play/PL8W2boV7eVfmdWs3CsaGfoITHURXvHOGm.html
I hope this helps!
Can we have a video on perturbation theory please
Thanks for the suggestion! We are planning a full series on perturbation theory, hopefully soon!
@@ProfessorMdoesScience oh please! :) these lectures are awesome giving great insights
Hello ma'am
What are reference books for basic ?
We like various books on quantum mechanics, including those by Sakurai, Cohen-Tannoudji, and Shankar. I hope this helps!