We consider Fermi's approach to quantizing the electromagnetic field. Errors: At 12:26 I say "plus i a-hat-minus a-hat-plus times ..." I should have said "plus i a-hat-minus minus a-hat-plus times ..."
I can safely say this channel was one of my main motivators for studying physics. I have just finished my course on introduction to quantum mechanics and I believe that without this channel's playlist on quantum mechanics I wouldn't have understood some important concepts as well as I did, and now that I am able to understand everything introduced in this channel I feel very excited with each video xD, thank you.
I'm currently studying theoretical physics and i think that trying to communicate to the world modern physics using a non trivial but accessibile language has to be an imperative both for scientist and students. I really like and deeply respect the work you are doing here. You found a very nice balance between mathematical stricness and clarity of exposition. Greetings from Turin, Italy. Alessandro
Another approach is to assume k is discrete and all functions are periodic. The sum is over a single period. Then we let the box grow infinitely large.
@@viascience I am confused about this same point. Is the summation over k a summation over every k pointing in every direction in 3d space? If this is the case, writing this as a sum instead of an integral over k looks wrong to me. (I also don't understand what you're getting at with the "another approach" in your reply.) How does one explicitly write the summation expression for k in this equation?
Thank you! :) Nice work, nice narration, slow calm and clear and yeah a nice and tight and accessible compilation of the mathematical machinery that is the quantization of the EM-field Keep it up! :)
These videos are excellent! I'm finding them the perfect complement to the textbook "Quantum Field Theory for the Gifted Amateur". Rewatching them carefully has filled in many gaps in my understanding of the topic.
Hoping on part c soon! I ended up finally getting a quantum field theory textbook thanks to the inspiration I got here and I’m gonna try and tackle Fermi’s little book.
May I ask why you get average of energy density to define the Hamiltonian? I think it should be integration of the energy density over the quantization volume? No? Thanks a lot for these efforts. They are crystal clear and simple
Errata: at 17:05 you say that q double dot is equal to "minus omega squared k". You should have said "minus omega squared q". The written equation is correct.
This is awesome! But one thing confuses me: at 10:45 you say that in place of x (the position of a unit mass), we have q, "the amplitude of an electromagnetic mode." But q isn't actually the amplitude of the mode (or anything else) as far as I can tell. *b* is the amplitude of the mode. So the "harmonic oscillator" becomes a bit more abstract than it was in the standing waves case, where the mode was separable into a time-dependent and space-dependent component.
Does anyone have contact info for the creator? The about is sparse and the Facebook link doesn't lead anywhere. But as a fellow educator I wanted to reach out to them.
The occupation number of a mode is the number of photons in that mode. This can be any non-negative integer: 0,1,2,3,... Alpha is an arbitrary index that labels the two possible polarizations. Usually, we use the values 1 and 2, but it could be any two numbers or symbols.
@@viascience Thanks for reply. I understand that occupation-numbers are non-negative integers. I meant to ask whether there is a occupation-number for every possible combination of 3 real numbers as components of k and one of 2 possible values of alpha. For example: is there a occupation number for k=( √2; √3;π)? Do occupation numbers remain non-negative integers after applying lorentz boost?
Oh, I think I got it. It is to index the different k-modes. Perhaps it should be subscripted to avoid confusion, otherwise it looks like is multiplying.
