Quantum Mechanics 12b - Dirac Equation II

[@viralllv]

This is awesome! Fun to see how quantum mechanics and relativity can coexist through this

[@MrOvipare]

This is very well explained... and it's a pretty subtle subject. Good job!!

[@tjejojyj]

Excellent. This deserves more views and your channel deserves more subs.

[@Bishop134265]

Keep these videos coming, I love them.

[@viascience]

+Jeremy Kerr Glad to hear it.

[@kevincleary627]

Best explanation I have seen. Excellent visual aids. So good that this presentation would be understandable without the lecture.

[@huonghuongnuquy7272]

I really love this lecture, it's very useful and well explained. Thank you so much

[@mistermxyzptlk3573]

Awesome clarity ! Thanks !

[@viascience]

You're welcome.

[@surendrabishwakarma7975]

Really,an amazing way of explaining,thankyou so much for this beautiful video.

[@viascience]

You are most welcome.

[@TheBigBanggggg]

As always in teaching these guys want to give you A GOOD FEELING. But there is more. Dirac's equation does not take into account quantum vacuum fluctuations (from QED) and therefore it can not explain the Lamb shift (in energy).

[@JosiahWarren]

You are great at presenting this ideas. Thank you

[@viascience]

You are welcome.

[@AMADEOSAM]

Very good content, keep on doing

[@factreviews9078]

The simplest and the best explanation corresponding to this topic..... Sir can you please upload the whole concepts of relativistic quantum mechanics?

[@viascience]

There is a series on quantum field theory. It's not complete, but I will eventually get to this.

[@vtrandal]

This might be obvious to others but I need help. At 9:50 into the video you say total angular momentum (J) is conserved but orbital (L) and spin (S) angular momentum are not. But J = L + S. So L gains whatever S loses and vice versa?

[@Artyom178]

What do you mean by "spin up or down" for the electron at rest? If electron doesn't move it hasn't a particular direction, so the spin can't have up or down.

[@bogdanghiorghiu5250]

Everything was nice and fine. WTF happened at 13:44?

[@davidschroeder3272]

It's a wonderful lecture, but for some reason it's out of focus on my screen, so the various symbols are hard to make out.

[@SquidKing]

at 5:03 I dont understand why the y and z components are dropped? is it because the electron is only moving in the x direction?

[@SquidKing]

oh yeah literally yeah well thats quite silly of me init

[@viascience]

Since the y component of momentum is proportional to the y derivative of the wavefunction, if there is only an x component of momentum we can drop any y or z derivatives in the equations.

[@llewellynhamiltoniiim.d.1057]

Quantum Mechanics by Albert Messiah 1959 is an excellent Book to learn QM advanced. 1100 pages. GL. French. Translated to English.

[@Papciopolak]

Question: solution for px!=0 is not normalized (sum of probabilities is larger than 1). Why, as it's clearly an error?

[@viascience]

+Ataleh To cut down on the number of symbols I left out normalization factors. I probably should have used a proportional sign rather than an equal sign. Technically, a plane wave cannot be normalized as its probability density is uniform throughout all space.

[@Papciopolak]

+viascience Thanks for the answer, it's all clear now.

[@2tehnik]

Not a fan of the natural units honestly. They aren't a problem for most of the video, just a bit inconvenient for someone like me to keep track. But for the stuff shown on the 6:35 slide, it kind of obscures what happens if you keep the units. For example, post differentiation, equation one should be: h-bar E Psi_1=h-bar c p_x a Psi_1+ mcˆ2 Psi_1 The Psi_1 term goes out leaving something sort of resembling the equation on the slide. Now, I assume the evident dimensional issue (energy is not dimensionally identical to energy times the h-bar dimesnion (momentum times length)) stems from the differentials not being dimensionally identical. Ie. Psi_1 is not the same (dimensionally) as Psi_1/length or time. But we cancel it out because it's the same mathematical function. That's a minor issue that is left unaddressed because of Natural units. But if you continue deriving this/solving for E you'll eventually get to Eˆ2=(p_x c)ˆ2+(mcˆ2/h-bar)ˆ2. And this clearly disagrees with what SR says the total energy should be. There's an h-bar component that shouldn't be there. This doesn't seem like something you could ignore. And I would like to know how it's averted or what I did wrong. I assume that the exponent of the Psi function is multiplied by 1/h-bar. Since I can see that solving the whole issue. But that's not evident at all as something one should do when it's all worked in purely in natural units. On a different note. I'm not sure why the total energy for the Psi_3 or 4 component would have to be negative. You still just get to the general solution of Eˆ2=(pc)ˆ2+(mcˆ2)ˆ2. So why do we assume only the negative solutions for E go? Is it an appeal to continuity since we know that E

[@peterpalumbo3644]

Negative energy states may have something to do with particles going back in time as opposed to forward. If Dirac predicts anti-electrons why not particles going back in time.

[@torresfan1143]

Actually, anti particles are known to be the form of our usual particles travelling backward in time only. Which is to say that if we have an electron and we say it's moving forward in time, then it's actually and perfectly right to say that it's antiparticle, the positron, travels backward in time. All in all, your reasoning is perfectly valid and clearly known. Famously, Carl Anderson reported positions as being electrons moving backward in time. Feynman also propagated this view a lot.

[@splazoplaza2987]

Because this would infer another dimension, not germane to the problem being solved, unless you are using string theory.

[@mattphillips538]

"...have the form e^-iEt where *CAPITAL E* is the energy"

[@taraspokalchuk7256]

why don't you enable the like button?

[@viascience]

+Taras Pokalchuk Fixed. Thanks for the heads up.

[@patrickboy8197]

Why there is description for all what u saying Remove what are u writing with black it's covering equations

[@viascience]

You might have subtitles turned on. Press the "CC" button to turn them off.

[@patrickboy8197]

@@viascience thnx Big up bro 💪

[@Sony187ful]

I don't uNderstand this

[@milroydissanayake886]

Go to hell