Understanding Quantum Mechanics #7: Atomic Energy Levels

Correction to what I say at 7 mins 20 seconds: These are the figures for m plus/minus 2, not (as I say) for m plus/minus 1. What's in the figure legend is correct.

The reference I mention at 6 mins 23 seconds is here:

In this video I explain how one calculates energy levels of electrons in orbits around atomic nuclei and why it doesn't really make sense to call them orbits. The images shown are actual solutions of the Schrödinger equation with a Coulomb potential.

#physics #education #science

0:00 Intro and Motivation
1:02 How the Calculation Works
3:05 Properties of the Solutions
7:39 Current Research
10:31 Sponsor Message

[tonyguerich]

I can't believe the number of times we still see the old animations of electrons "orbiting" anround the nucleus, often with the comment "like planets around the sun" And often from explainers who surely know better. I could pull my hair out if I had any left. Thanks for your careful explanations

[AndrewBlucher]

This is how to communicate science. By explicitly stating the simplifications you enable the student to
a) understand the limit of their new knowledge, and
b) know what to study to extend that knowledge.
Well done Sabine, as always.

[wholenutsanddonuts]

That graph at 5:30 is a brilliant visual way to show that electron “shells” are much more spread out than we’re taught. Thank you!

[gustavoaroeira]

I love this video as I am a graduate student in Quantum Chemistry! Quantum mechanics allows chemists to simulate reactions mechanisms and compute properties such as free energy, enthalpy, entropy, equilibrium constants, etc. Due to difficulty of running precise computations, only recently, with the improvement of our approximations, traditional experimental chemists started to be interested on what quantum chemistry can offer.

[clermeil]

These videos are my favorite part of Saturday morning! (East coast US)

[jeffdavis]

I don't have a clue what she's talking about but I keep listening and listening.

[TwistedSoul]

Chemistry is just the physics of the valence electrons.

[x_abyss]

Fantastic! I can't tell you how long I've waited for such a video that relates Schrödinger's equation with spherical harmonics to explaining bulk plasma resonance with GR. Thank you Sabine.

[jonashartmann]

I just want to add that calculating properties of molecules has gotten so important that nearly every chemistry phd student has to do it at least once during their studies. Even if they are experimentalists

[mikemackie]

Loved the video Sabine. Especially the part when you said "I love it because it never would have occurred to me". We're all approaching the topic from a different levels of understanding and you nail the delivery 💛

[lastspring]

The patterns always remind me of the Chladni plate resonance demonstrations. Interesting to look at.

[jonahansen]

Thanks Sabine, that was great. I took Physical Chemistry 50 years ago, so I'm not totally lost, but it sure brought out how much I've forgotten.

[troyhiscock]

"Fun Fact: Without Special Relativity, Gold would not look gold"
Are you just going to drop that on us and move on like nothing happened?

[seetheious]

The visualizations are very helpful, the explanation clear and concise, mentioning the complications and what issues arise makes it more interesting. Great video.

[ramuthra]

Sabine, I want to say a massive thank you. Thank you for having a healthy respect for the intelligence and curiosity of your audience. Thank you for not dumbing your explanations down to the point they're inaccurate. And thank you for taking a stand to fight against the shameful amount of BS and pseudoscience that exists online. You get straight to the point and I come away feeling like I've actually LEARNT something - it's a breath of fresh air, and as I hope I've made clear already; I can't thank you enough.

[RWin-fpjn]

This is a great video, explaining in clear terms the mathematical description of the atom orbiting electron in its various states. But Sabine was close to making it even much better. At 6:00 into the video Sabine mentions that the wave function avoids divergence for r=0 rather like we see in singularities. Well, let's actually go this path (as per Einstein's equivalence principle). Let's for a moment suggest at the core of EVERY atom there is indeed a micro-singularity. If so, then from academic simulations (Karas, Kapacek e.a. 2012) we next know what happens to straight EM fieldines around rotating micro-singulities; they get bend, folded and this fold next get wrapped in orthogonal spirals with finite windings, the number of which relating to the energy (momentum) involved. At their farthest point (energy wise) these spiral end folds cross the micro event horizon into our ST world where they discharge as a double (a fold always has two intersections) energy charge we observe as 'electron'. After this the EM fieldline would unwind and wind up anti-clockwise at the other side, causing the next double discharge at the other side of the electron orbit. This is actually photographed at the Max Planck Institute Heidelberg with a He atom. Crucially our oblique view of this wound up spiraled EM fieldline would appear to us as an INTEGER or 'quanta' of windings. This provides a perfect explanation for the century old issue of what quanta are. Finally, we should notice that the spiraling of individual fieldines, will cause their orthogonal straight form to contract to provide the material. If we accept that EM fieldlines in their straight orthogonal form are tangible spacetime fieldlines than we now have an explanation for ST contraction caused by atoms; the oscillating 'quantized EM spirals' always cause a net shrinkage of the orthogonal ST fielding. leading to the sensation we call 'gravity'. As such we may notice the spin 1/2 of the electron will appear spin 1: 1/2 =spin 2 from this orthogonal ST contraction viewpoint. Graviton anyone? It would appear with all these pieces of the puzzle coming together that indeed this is the tangible physical setup that belongs to the mathematical description of this video...

[michaelblacktree]

Back in high school, they taught the "planetary" atomic model. That was in the 1980s. But even then, the quantum model was already ubiquitous. I didn't learn about the quantum model until many years later. I feel like I missed out.

[paulkohl]

It is amazing how much mileage scientists get out of the Hydrogenic States. Interesting video.

[bozo]

Thank you for the 3D representation. I had always wondered... and mostly still do, but that was helpful.

[shubhsrivastava]

7:56
"Calculating atomic energy levels was a frontier research a century ago. Now, it's just a practice for Physics students"
This fact in itself tells about the great advancements in science and technology we have had in the past century. It's Great! 👍🏻