Quantum Mechanics 12a - Dirac Equation I

[@everettvacek1]

Currently struggling through graduate quantum mechanics. This was a HUGE help!

[@viascience]

Glad to hear it helped.

[@mudkip_btw]

Your videos are so full of information that is hard to find out about by yourself. Thanks so much!

[@viascience]

You are most welcome.

[@themasstermwahahahah]

incredibly straightforward and comprehensive, by going in a linear order of concepts, if i dont know something, i can just learn it, come back to the video and be able to follow

[@xenmaster0]

Absolutely superb. Clearest and most beautiful explanation of the Dirac equation I've seen.

[@viascience]

Glad you enjoyed it!

[@jackson_mcgrath]

This was a great, thanks again for all the high quality educational videos. Anxiously awaiting part two

[@viascience]

+Jackson McGrath Thanks for the encouragement.

[@DevashishGuptaOfficial]

This is the best explanation for the Dirac Equation, on the KZbin!

[@viascience]

+Devashish Gupta Thank you.

[@Cosmalano]

Wonderful video and wonderful to see a new addition to the series.

[@viascience]

+electrocat1 Thanks.

[@herbiepop]

A consistently high quality series.

[@viascience]

+herbiepop Gracias.

[@roberthuber2770]

In 17 minutes you have created a quantum mechanics addict... thank you!

[@titikshadua155]

Thankyou for this. One of the best course videos!

[@michaelfox9675]

The second line beginning at 8:25 is invariant under every permutation of {Sx, Sy, Sz}, but the third line isn't, and doesn't satisfy the second line, which it supposedly is a solution of.

[@viascience]

The Sx, Sy, Sz matrices given in the third line satisfy the commutation relations given in the second line.

[@tachyon3.14]

I might not understand this fully yet but imma come back to this many times

[@floriandobai4486]

Thank you, for this great video, your work is highly appreciated.

[@viascience]

You are most welcome.

[@remusgogu7545]

WOW. One of the best presentation for the subject. WOW. Really, thanks for making this video 🧡

[@viascience]

You are most welcome.

[@nicolasPi_]

Witnessing the mathematical derivation that led to the introduction of spin and antimatter is like opening a window to the fabric of reality.

[@jiadong7873]

This is one of best QM video series I have ever seen. From electron to atom, then to molecule. Very impressive, thank you so much for your effort. I am wondering if there will be a 'from molecule to solid' series which related to density functional theory or something similar? :)!!! @viascience

[@ryanamiri8652]

that sounds cool

[@vaishalitrivedi2461]

Yes i agree

[@MindMatriX]

​@@vaishalitrivedi2461 hehehe

[@MindMatriX]

Hiiiiiiii

[@vaishalitrivedi2461]

@@MindMatriX hlo

[@victorzzz24]

REALLY REALLY LOGICAL AND CLEAR!

[@vtrandal]

At 3:00 minutes in this wonderful video you explain slope and curvature using a triangle and ball (circle in R2). What is curvature in higher dimensions and what geometric shape relates to it? Is it just an n-ball in Rn? Or is there some “hyper” shape we can try visualize for curvature of curvature in R3 or R4 and so on?

[@viascience]

That a complicated subject. Different "measures" of curvature can be used to represent different quantities of interest. In the Relativity series there are lectures on Differential Geometry (kzbin.info/www/bejne/poarpmmqrMRkg8U) that deal with curvature in higher dimensions.

[@vtrandal]

@@viascience I studied electrical engineering years ago. The Dirac delta was used to get the Impulse Response of a linear system. I’m eager to see if Dirac used the delta “function” in quantum mechanics and especially in relation to the Dirac equation. Do you talk about the Dirac delta in any of your videos?

[@wrox2757]

Which reference books should i use along this series? This video is amazing and I'm planning to watch from the start. Thanks.

[@SquidKing]

Amazing video! Unfortunately I am lost at 8:18 where you say we can derive ^Sx and ^Sy by using the cyclic commutation relationships. I try to set ^Sy equal to a 2x2 matrix A B C D, but I can't seem to find solutions for B or C using your suggested method.

[@viascience]

Set Sx=[A,B;C,D]/2 and Sy=[E,F;G,H]/2 (where , separates columns and ; separates rows). The commutator relations [Sy,Sz]=iSx and [Sz,Sx]=iSy require that A,D,E,H are all zero and F=-iB, G=iC. Then [Sx,Sy]=iSz requires that and C=1/B. This leaves us with Sx=[0,B;1/B,0]/2 and Sy=i[0,-B;1/B,0]/2 . Then you can argue by symmetry that B=1.

[@SquidKing]

@@viascience Thankyou so much for this! It turned out I still had difficulty solving for B until I learnt that the matrices had to be hermitian. This series is by far the best easy-to-digest QM material on the internet. I would not have been able to dive nearly as far into QM without your help and I am very grateful. Thankyou!

[@jamesgrandoff9600]

Thanks for the video. Very informative. It appears to me that both Dirac and Feynman assumed that time had the properties of being both positive and negative. Has anyone sought to address the concept of time being only positive and in the range 0 to C? My thinking was that negative energy trapped in zero time (i.e. cannot react) would be a possibility and I was hoping to explore that topic. Please let me know if there are any papers or sources relevant to that concept. Thanks again.

[@mateomaderas5504]

It may seem like nitpicking, but the curvature of a curve is NOT the inverse of the second order derivative of that curve.

[@viascience]

I don't think I ever say curvature is the inverse of the second derivative. Typically the curvature of a circle is taken to be the inverse of its radius. The curvature of y = f(x) is y''/(1+y')^(3/2), which for small y' is approximately y''. At 3:22 I use an "approximately equals" sign to indicate that the curvature is approximately the second derivative. But I should have said "the curvature is _approximately_ the derivative of the derivative." I left out the "approximately" when I spoke.

[@mateomaderas5504]

All good my crappy eyes didn't spot the curly equals either

[@DidiestEva]

at 12:00, why can the value of \int |psi|² dV change ?

[@muhammadazhar3505]

Plz explain Dirac equation at quantum Field Theory. Good work.

[@viascience]

We will get to that in the Quantum Field Theory series.

[@dexio85]

Another very good video. Thanks!

[@viascience]

+dexio85 You're welcome.

[@johngibbons494]

Great videos. Thank you. About 4mins into this video you bring up operators. I can't find the video on angular momentum you mentioned that helps describe operators. Could you please refer me to the title that explorer this . Thank you in advance

[@viascience]

You are welcome. See kzbin.info/www/bejne/hKjFp4eXZ92Jb80 , kzbin.info/www/bejne/bYDQp4OvnMlmn7s and kzbin.info/www/bejne/iKDUanx3bL9ghrs

[@justanotherguy469]

Thank you for this clear and concise lecture.

[@Hack3r91]

15:38 I have known Dirac matrices to have a minus sign on the bottom-left Pauli matrices, are these another basis?

[@viascience]

+Alessandro Porcelli You get those forms if you multiply all four matrices on the left by the beta matrix. The four matrices are then usually denoted by gamma: gamma_x = beta*alpha_x etc. You get the same solutions, but the equations have a different, usually considered more convenient, form.

[@Hack3r91]

Thank you for the explanation, very good job with this channel!

[@vasanthrajaram1241]

how did h get canceled while substituting energy in momentum operators in 15:54? the only way it can get canceled is if we multiply h over h in (m.beta.wave function) the last term in Dirac equation. great video

[@markhamilton8728]

Great job! Dr W

[@viascience]

Thanks.

[@olgermannik1830]

10:15 should this not be sum of squares of 1. deriatives?

[@viascience]

Are you referring to the "nabla squared" symbol (the "Laplacian")? That is the sum of the second derivatives. The first derivative operator operating on the first derivate operator is the second derivative operator - the derivative of the derivative.

[@olgermannik1830]

@@viascience Yes I meant that. I know that Laplician means (d/dx)^2+(d/dy)^2+(d/dz)^2. My first misunderstanding was whether you substituted energy and momentum with corresponding operators applied on wavefunction and then squared or substituted only operators and then put wavefunction to right side of expression. I first thought you meant the first, but now I understand that you meant the second. Secondly I did not realise that ^2 meant scalar product. If these 2 are correct, then I now understand it.

[@IIPlayingGodII]

why do terms of the form \alpha_i * \beta * p_i * m vanish on 13:51? great video by the way :D

[@johnchristian5027]

Brilliant video!

[@themightyripples6582]

This has likely been answered... at around 2 minutes there is an infinite sum, how would this be expessed in sumation notation, i.e., capital sigma notaion?

[@abednadir8437]

Absolutely Brilliant!

[@jasonarakawa2171]

Great video! Thanks!

[@viascience]

+Jason Arakawa You are welcome.

[@renumalik3096]

Fabulous explanation

[@viascience]

Thanks

[@TheRumpusView]

Oh golly! I am vaguely familiar with the Dirac use of matrices to determine negative energies etc, but golly, this video is scary and requires me to revise all sorts of stuff to comprehend the logic and the maths. I have even forgotten what ">" does! What software do you use to present the equations? And you must be some sort of physics professor to have the level of understanding you have.

[@viascience]

+TheRumpus I use libreoffice presentation (open-source alternative to Microsoft PowerPoint). It has a decent math editor.

[@blockhead1899]

I tried my absolute hardest to follow the math but there is so much I don’t understand and this is supposed to be the basics??? Do you know any videos that explain the math more indeph for beginners pls?

[@daydreamer05]

How long did it take you to make this video?

[@Giovanni2862]

Could you recommend a book on the subject?

[@nintendoswitchfan4953]

This video saved my life

[@omarfarukh8200]

Sir, great lecture but am from biology background I need step by step explanation of the mathematics involved in Dirac equation, if you send me a notes also it will be okay for me

[@hello-world2023]

Excellent!

[@lixiaojiang8182]

Hey, nice talk, can you share the slides with us ? thank you very much!

[@realimage3656]

good!

[@vaishalitrivedi2461]

Very nice vdo👌👌

[@jordanweir7187]

Thanks for the vid dude

[@viascience]

UR welcome.

[@sayanchakraborty1945]

I have always felt that Dirac equation is fundamentally flawed. It somehow explains properties of electrons, however it badly fails when you try to explain similar properties for other particles, such as protons. for example it gives an accurate measure for the g value of electrons, when you take the non relativistic limit of dirac equation under minimal coupling prescription i.e. essentially the pauli equation, but it abysmally fails to reproduce g values for other particles.

[@Arch497]

Didn't knew George Carlin did quantum mechanics equation descriptions

[@abidmessoud9767]

very wonderfull course than you very much

[@saikiranalvala502]

Thank you so much for this sir🙏🙏🙏

[@viascience]

You are welcome.

[@Shine_with_devine_light]

Thank you very much.... 😊

[@mauriciofurlan7773]

Poderia colocar legendas em portugues

[@SafetySkull]

If the dirac equation is this simple, then why do people act so coy and shy every time you ask them what a spinor is?

[@knowledgesman3167]

thank you! highest level !

[@sajateacher]

I thought that negative energy was just gravity. I mean, it does everything the opposite that energy does.

[@Quintinohthree]

Energy: The capacity for doing work, i.e. exerting a force over a displacement. Gravity: Force acting on objects with mass, which is equivalent to energy. They don't seem opposite to eachother, not even orthogonal to eachother but interdependent.

[@sajateacher]

I read it in a book somewhere, I'll try to find the title. If you have a source of energy, such as the thermonuclear energy in a bomb, matter is going to be repelled from the centre, whereas with a source of gravity, matter will be attracted towards the centre.

[@Cosmalano]

+Ryan Blais a force is the negative gradient of potential energy.

[@viascience]

+Ryan Blais The negative energy solutions to the Dirac equation are for an isolated particle, hence without reference to interactions with other particles.

[@sajateacher]

Thanks electrocat1 and viascience for clarification. I think I read it in a Time Life book, but here is essentially the same idea. plus.google.com/105977048411460572598/posts/TRZz4cCZKe8

[@briangarcia4053]

I wish I was smart enough to understand any of this

[@JosiahWarren]

Amazing

[@ronaldjorgensen6839]

thank you

[@tanvirfarhan5585]

omg what a great video

[@geraldinejasnin7378]

possible en francais !!

[@Nolrai12]

I just want to say I specifically watch these videos _because_ they have the math.

[@ryanamiri8652]

thats super cool

[@aprylvanryn5898]

You may as well have been speaking Greek. I'm so lost but rest assured I will be back once I've leveled up.

[@ariayahaile440]

Ask Leonard Susskind a specific physics question, including "What is the Dirac equation?" - askkindly.thanksci.com

[@TimeDesignsMedia]

Neither particle exists in linear time.

[@hadijaffri9856]

Im a highschool student,dont know why im watching this at 3:30am

[@Kenbreg]

x,y, zed would have been nice. Not x,y,zee

[@arthurbarbosa5825]

I'm 14, why am I here at 2am?

[@MAandS]

I'm here because of Death Stranding.

[@David_Lloyd-Jones]

Kwannamechanics. Who knew?

[@brianmenendez]

Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality. Nikola Tesla

[@szeredaiakos]

assHat .. right .. :P

[@shaquilleoatmeal2685]

Anyone here feel like an idiot after watching this video?

[@makaylawilson2801]

Hi

[@vasanthrajaram1241]

how did h get canceled while substituting energy in momentum operators in 15:54? the only way it can get canceled is if we multiply h over h in (m.beta.wave function) the last term in Dirac equation. great video

[@viascience]

See 12:30 - we use units in which h-bar is one.

[@vasanthrajaram1241]

oh thank you so much sir. I almost forgot about it. thank you for making this so much clear.

[@vasanthrajaram1241]

oh thank you so much sir. I almost forgot about it. thank you for making this so much clear.