Dirac Equation | Derivation and Introduction

References:
[1] Sakurai, Napolitano, "Modern Quantum Mechanics".

Table of Contents:
00:00 Different Hamiltonians
00:35 Ansatz
01:01 Finding the Coefficients
01:49 Finding Beta
02:02 Relation Between Alpha and Beta
02:30 Finding a Relation For Alpha
03:11 Matrices?

▶ Music ◀
TheFatRat - Fly Away feat. Anjulie

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[nuclerpenguins]

Hi @Pretty Much Physics, this was a great video but I was confused at the 2:20 mark where we find out that {ak, B}=0.

How can you switch the indices on the second ajpj term to akpk? Did we not assume that akpk and ajpj are distinct from one another (how can you "just" switch them?)? I'm probably missing something in the reasoning and am curious to find out why this is true.
(if you do see this comment on a two year old video lol)

[coreytaylor]

cant wait to be able to understand that math

[roneyandrade]

Watching this video on my birthday is truly the best birthday present.

[sruthis]

Every physics related topics are usually around 45min to more than hours duration. But these videos are very short and includes all contents without fail. Thank you so much Sir🙏. Keep adding videos Sir

[TheDummbob]

I don't quite understand how the trick at 2:40 works:
Is it required that pj commutes with ak?
And if so, how can i know that they do commute at this point, there's almost nothing known about the algebra of the ak (yet)

[shreyasdillon]

Hi so this might be a stupid question but why did you sum from 0-3? I'm guessing it's because 4 dimensions with time and 3 space but wasn't sure. Thanks for the great video!

[juliettegeo]

Question for the last condition where {alpha_k, alpha_j} = 2 \delta _j, k . Of course this makes sense for j = k. When j != k, then the whole left side goes to 0. In this case the only way for the equation to hold true is if the momentum is also 0? So if the particle isn't moving at all? and is perfectly localized?

[ollie]

you should use a finer pen tip to make it slightly clearer

[Masterdoctorgenius]

Hi,

can any1 explain at 1:25 where does alpha_j p_j come from when you square H. Why does it not remain alpha_k like in the first term?

[sagarvidu]

which book or note should I follow for reading this stuff?
Any suggestions??

[varunv]

This seems to be uni level/physics degree equation. Can't wait to study it in depth someday when I eventually go to uni.

[xenmaster]

Fine explanation...as far as it goes. What this explanation does not explain, alas, is: 1) why is the Dirac equation a first-order equation instead of a second-order equation? Logically, you'd expect that since we're dealing with the Hamiltonian, it would have to be a second-order equation. In classical mechanics, we obviously get second-order equations since Newton's force law involves a second derivative. We know it can't be a higher order derivative because Ostragradski's theorem says higher order derivative terms leads to energy being unbounded below. So where does Dirac come up with the first-order equation?
2) Where do the creation and annihilation operators come in? This seems to arrive from left field. I get physically why they're needed (to account for particle decay) but where do they come from _mathematically_?

[nellvincervantes]

Question sir. Is electron always apply quantum field theory (quantum mechanics + special relativity) cause particles can be wave and de broglie wavelength is derived from E^2 = m_o^2 c^4 + p^2c^2 (which is the energy for special relativity) ?

[terminate]

Why is the commutator of alpha_k and aplha_j equal to a Kronecker delta? I don't fully see the reasoning behind this.
Also, the equation wasn't fully derived. To my understanding, you have to mess around with Dirac matrices "4X4" to get to the final result, though I'm not sure how that's done.

[nellvincervantes]

Or the oscillator is non relativistic if hamiltonian is schrodinger and relativistic if hamiltonian is klein-gordon? Sorry sir I got stuck in this problem.

[user.-ksdl]

Nice vid, vid.
Your accent and pronounciation of the word "Ansatz" sounded german, thus may i ask if you're german.
I know the vid is old af

[kingdomofknowledge]

Make a documentary about dirac equation from its origin ! And please use animations ! It will be great if some equation can be explain through animations :- Relativity, schrodinger, dirac equation !

[pauldirac]

Phew . That gave me a bloody headache. Again.

[physics_enthusiast_Soorya]

I'm waiting to understand that maths

[epitome]

Why Math seems too Ez when calculations don't involve :l