L4.4 Dirac equation for the electron and hydrogen Hamiltonian
ฝัง
- เผยแพร่เมื่อ 13 ก.พ. 2019
- MIT 8.06 Quantum Physics III, Spring 2018
Instructor: Barton Zwiebach
View the complete course: ocw.mit.edu/8-06S18
TH-cam Playlist: • MIT 8.06 Quantum Physi...
L4.4 Dirac equation for the electron and hydrogen Hamiltonian
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2:38 He went from Dirac to Borat.
VERY NICE
MY WIFE
😂😂😂 ...
BRUHHHHHH
This comment is absolute gold
great, I finally understood why 4x4 matrices and their anticommutation relation. The teacher is a good explainer.
too bad the subject is useless
@@lugia8888Too bad you're useless
@@lugia8888seriously…..without this understanding of the nature of things, you wouldn’t have the device you used to post the comment, nor indeed the internet, just a few things in the modern world you wouldn’t have….
Charles Galton Darwin (the physicist) was indeed the grandson of Charles Robert Darwin (the naturalist).
So this is what my professor here at University of Toronto meant by in order to consider magnetic effects in the hydrogen atom one must introduce relativity.
I like to thank professor Barton Zwiebach for the explanation. kind regards.
Dirac was way ahead of his time. He was the modern Einstein.
modern??? He was a contemporary of Einstein!
Dirac used math, not concepts, to predict reality. Einstein was a thought experiment, conceptual guy long before he mastered the math. They literally knew each other and both were well aware of the other's brilliance.
@@ricomajestiche was 23 years younger, so they were in some sense contemporaries. In a lot of ways Dirac was part of a different generation however. Consider that Einstein’s initial paper on relativity was published when Dirac was 3
At 6:32 what if 1 were the pie of a quantum particle and that was its vector?
13:53 thanks for clearing that out...for a moment I got confused lol
thank you🙏
nothing can replace traditional old-school blackboard and chalk.
R U saying that all those chalk powder he breath in is good for his lungs?
A white board and non-permanent marker? What a stupid comment to make.
@@Tommybotham Yours is far stupider. IYKYK
@@hwytubejust breath away from the board
@@Tommybothamnot really a stupid remark, white boards and markers require a lot of plastic which is not eco-friendly
Pure genius.
Que bien ... !
Este Profesor no lo mencionan me parece Barton una leyenda de la UNI en Lima Peru...hizo su Tesis un ciclo antes de acabar la carrera de Ing. ELectronica un imposible ahora..en estos tuempos..
This course in my uni was taught with a power point presentation. I'm glad MIT still uses the good old blackboard. This teaching style is the only one that works and no amount of technology can replace it. The overuse of powerpoint presentations is actually harming education.
Shouldn't, in the Dirac's representation, the sigma matrices on the second row be negative?
These aren't the gamma matrices. Those are obtained my multiplying both sides of the equation by the "beta" matrix to move the non-identity matrix from the rest energy term to the time derivative. That multiplication adds the negative sign in Dirac representation of the gamma matrices. We want to avoid the covariant form here because we want to be able to interpret the Dirac equation as a time independent "Schrodinger equation" whose eigenvalues we can interpret the same way.
...you lost me at 'shouldnt' haha
love
Wow
I was told MIT still uses green boards but why?
I trust MIT so I wish to receive a reply!
Yes, MIT still uses blackboards and green boards. Here is video explanation by Sanjoy Mahajan from MIT 5.95J Teaching College-Level Science and Engineering, th-cam.com/video/QcRteDU9Eco/w-d-xo.html. We hope this helps you!
@@mitocw I watched this and was surprised that perhaps the most important reason was not given.
Slides are passive. Taking notes from a blackboard is "thrice" active.
When person takes notes in their own handwriting, they are being forced to fully process the information visually watching the speaker and what is being put on the board, auditorially at what is being said and what emphasis is given, and kinestheticly as their had is actively transcribing all that is being said and what is on the board. The threefold active pathways stimulate learning. Writing on a slides is at best 20 - 30% of this.
Is this hard/difficult? Sure it can be. But when students practice this over and over, they can and do become quite proficient.
And as an adult, when did your boss last come to your cubical with a slide deck of your next assignment. He tells you -- you write it down. Taking notes in school is good practice for the "real world."
@@mitocw your system work is amazing
por primera vez diré esto de forma no irónica, ORGULLO PERUANO xd
why is the dirac equation not dependent on the representation of the alpha, beta matrices? different representation, different physics?
Because there's a linear map between both representations, the space formed by one is homeomorphic to the formed by the other. In other words, physics is the same on both bases.
@@alchamiwa LOL. Complete gibberish.
@@ArnoldSommerfeld it's not, actually
@@alchamiwa Of course it is. You have no idea what you are talking about.
@@ArnoldSommerfeld say that to my masters degree
It’s not as easy as it looks.
LOL.
If it isn't ez for you, It doesn't mean it will be difficut for us, too.
The Pauli Exclusion Principle.
Dirac is easy, and because of that it causes issues that are not easy. In mathematics, we call it a generalized function because it extends the idea of a function past the classical notion. In a an engineering, it is not easy in application as you would think. I understood what you meant….
Dirac is easy, and because of that it causes issues that are not easy. In mathematics, we call it a generalized function because it extends the idea of a function past the classical notion. In a an engineering, it is not easy in application as you would think. I understood what you meant….
he jumped from the pauli hamiltonian to E_s(chi) equation
I lost it after he was done dusting the board.
Let's celebrate these 33 seconds of dusting: 0:05
All that work just to compute energies which agree with experiment only less than a percent better than you would using just the Schrodinger equation.
And that proves that we strive for accuracy no matter how tedious it is.
Antimatter wtf
Sir you belong which country? Good explain
Peru
Conservation of Spatial Curvature (both Matter and Energy described as "Quanta" of Spatial Curvature)
Is there an alternative interpretation of "Asymptotic Freedom"? What if Quarks are actually made up of twisted tubes which become physically entangled with two other twisted tubes to produce a proton? Instead of the Strong Force being mediated by the constant exchange of gluons, it would be mediated by the physical entanglement of these twisted tubes. When only two twisted tubules are entangled, a meson is produced which is unstable and rapidly unwinds (decays) into something else. A proton would be analogous to three twisted rubber bands becoming entangled and the "Quarks" would be the places where the tubes are tangled together. The behavior would be the same as rubber balls (representing the Quarks) connected with twisted rubber bands being separated from each other or placed closer together producing the exact same phenomenon as "Asymptotic Freedom" in protons and neutrons. The force would become greater as the balls are separated, but the force would become less if the balls were placed closer together. Therefore, the gluon is a synthetic particle (zero mass, zero charge) invented to explain the Strong Force. An artificial Christmas tree can hold the ornaments in place, but it is not a real tree.
String Theory was not a waste of time, because Geometry is the key to Math and Physics. However, can we describe Standard Model interactions using only one extra spatial dimension?
What if we describe subatomic particles as spatial curvature, instead of trying to describe General Relativity as being mediated by particles? Fixing the Standard Model with more particles is like trying to mend a torn fishing net with small rubber balls, instead of a piece of twisted twine.
Quantum Entangled Twisted Tubules:
“We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct.” Neils Bohr
(lecture on a theory of elementary particles given by Wolfgang Pauli in New York, c. 1957-8, in Scientific American vol. 199, no. 3, 1958)
The following is meant to be a generalized framework for an extension of Kaluza-Klein Theory. Does it agree with the “Twistor Theory” of Roger Penrose, and the work of Eric Weinstein on “Geometric Unity”? During the early history of mankind, the twisting of fibers was used to produce thread, and this thread was used to produce fabrics. The twist of the thread is locked up within these fabrics. Is matter made up of twisted 3D-4D structures which store spatial curvature that we describe as “particles"? Are the twist cycles the "quanta" of Quantum Mechanics?
When we draw a sine wave on a blackboard, we are representing spatial curvature. Does a photon transfer spatial curvature from one location to another? Wrap a piece of wire around a pencil and it can produce a 3D coil of wire, much like a spring. When viewed from the side it can look like a two-dimensional sine wave. You could coil the wire with either a right-hand twist, or with a left-hand twist. Could Planck's Constant be proportional to the twist cycles. A photon with a higher frequency has more energy. ( E=hf, More spatial curvature as the frequency increases = more Energy ). What if gluons are actually made up of these twisted tubes which become entangled with other tubes to produce quarks. (In the same way twisted electrical extension cords can become entangled.) Therefore, the gluons are a part of the quarks. Quarks cannot exist without gluons, and vice-versa. Mesons are made up of two entangled tubes (Quarks/Gluons), while protons and neutrons would be made up of three entangled tubes. (Quarks/Gluons) The "Color Charge" would be related to the XYZ coordinates (orientation) of entanglement. "Asymptotic Freedom", and "flux tubes" are logically based on this concept. The Dirac “belt trick” also reveals the concept of twist in the ½ spin of subatomic particles. If each twist cycle is proportional to h, we have identified the source of Quantum Mechanics as a consequence twist cycle geometry.
Modern physicists say the Strong Force is mediated by a constant exchange of Mesons. The diagrams produced by some modern physicists actually represent the Strong Force like a spring connecting the two quarks. Asymptotic Freedom acts like real springs. Their drawing is actually more correct than their theory and matches perfectly to what I am saying in this model. You cannot separate the Gluons from the Quarks because they are a part of the same thing. The Quarks are the places where the Gluons are entangled with each other.
Neutrinos would be made up of a twisted torus (like a twisted donut) within this model. The twist in the torus can either be Right-Hand or Left-Hand. Some twisted donuts can be larger than others, which can produce three different types of neutrinos. If a twisted tube winds up on one end and unwinds on the other end as it moves through space, this would help explain the “spin” of normal particles, and perhaps also the “Higgs Field”. However, if the end of the twisted tube joins to the other end of the twisted tube forming a twisted torus (neutrino), would this help explain “Parity Symmetry” violation in Beta Decay? Could the conversion of twist cycles to writhe cycles through the process of supercoiling help explain “neutrino oscillations”? Spatial curvature (mass) would be conserved, but the structure could change.
=====================
Gravity is a result of a very small curvature imbalance within atoms. (This is why the force of gravity is so small.) Instead of attempting to explain matter as "particles", this concept attempts to explain matter more in the manner of our current understanding of the space-time curvature of gravity. If an electron has qualities of both a particle and a wave, it cannot be either one. It must be something else. Therefore, a "particle" is actually a structure which stores spatial curvature. Can an electron-positron pair (which are made up of opposite directions of twist) annihilate each other by unwinding into each other producing Gamma Ray photons?
Does an electron travel through space like a threaded nut traveling down a threaded rod, with each twist cycle proportional to Planck’s Constant? Does it wind up on one end, while unwinding on the other end? Is this related to the Higgs field? Does this help explain the strange ½ spin of many subatomic particles? Does the 720 degree rotation of a 1/2 spin particle require at least one extra dimension?
Alpha decay occurs when the two protons and two neutrons (which are bound together by entangled tubes), become un-entangled from the rest of the nucleons
. Beta decay occurs when the tube of a down quark/gluon in a neutron becomes overtwisted and breaks producing a twisted torus (neutrino) and an up quark, and the ejected electron. The production of the torus may help explain the “Symmetry Violation” in Beta Decay, because one end of the broken tube section is connected to the other end of the tube produced, like a snake eating its tail. The phenomenon of Supercoiling involving twist and writhe cycles may reveal how overtwisted quarks can produce these new particles. The conversion of twists into writhes, and vice-versa, is an interesting process, which is also found in DNA molecules. Could the production of multiple writhe cycles help explain the three generations of quarks and neutrinos? If the twist cycles increase, the writhe cycles would also have a tendency to increase.
Gamma photons are produced when a tube unwinds producing electromagnetic waves.
The “Electric Charge” of electrons or positrons would be the result of one twist cycle being displayed at the 3D-4D surface interface of the particle. The physical entanglement of twisted tubes in quarks within protons and neutrons and mesons displays an overall external surface charge of an integer number. Because the neutrinos do not have open tube ends, (They are a twisted torus.) they have no overall electric charge.
Within this model a black hole could represent a quantum of gravity, because it is one cycle of spatial gravitational curvature. Therefore, instead of a graviton being a subatomic particle it could be considered to be a black hole. The overall gravitational attraction would be caused by a very tiny curvature imbalance within atoms. We know there is an unequal distribution of electrical charge within each atom because the positive charge is concentrated within the nucleus, even though the overall electrical charge of the atom is balanced by equal positive and negative charge.
In this model Alpha equals the compactification ratio within the twistor cone, which is approximately 1/137.
1= Hypertubule diameter at 4D interface
137= Cone’s larger end diameter at 3D interface where the photons are absorbed or emitted.
The 4D twisted Hypertubule gets longer or shorter as twisting or untwisting occurs. (720 degrees per twist cycle.)
How many neutrinos are left over from the Big Bang? They have a small mass, but they could be very large in number. Could this help explain Dark Matter?
Why did Paul Dirac use the twist in a belt to help explain particle spin? Is Dirac’s belt trick related to this model? Is the “Quantum” unit based on twist cycles?
I started out imagining a subatomic Einstein-Rosen Bridge whose internal surface is twisted with either a Right-Hand twist, or a Left-Hand twist producing a twisted 3D/4D membrane. The model grew out of that simple idea.
I was also trying to imagine a way to stuff the curvature of a 3 D sine wave into subatomic particles.
.
You need serious help
Crackpots be like
Which book he uses?
The syllabus states the required text is: Griffiths, David J. and Darrell F. Schroeter. Introduction to Quantum Mechanics. Cambridge, United Kingdom: Cambridge University Press, 2018. ISBN: 9781107189638. For more info and materials see: ocw.mit.edu/8-06S18. Best wishes on your studies!
@@mitocw I have the 3rd edition and there is only one mention of the Dirac Equation on p. 304, Problem 7.22. That's it!
He also mentioned Shankar (Principles of Quantum Mechanics).
the inaudible at 10:39 is say
Thanks for your note! The caption has been updated.
Easy 😊
Next is psychics
What's the name of this professor?
Professor Barton Zweibach-it’s listed in the information below the video^^
@@mitocw He's really a hard working and industrious professor!!! Love you Sir!❤❤
Professor Barton Zwiebach is peruvian, from Lima, Peru
@@luismontalvohiroyasu5814 He's a pretty smart cookie!
500 first!
28 × 3 + 63 × 4 = 336
Eh?
It so easy
Same guy that writes IKEA instructions
So you have high atom pusher go high low normal formula pusher it can go high but speed go up so this formula mostly is about pusher
I'm a genius.
Not unless I say so.
nth comment
Here because of a clip of Weinstein on Rogan.
Deficult to understand this topic Dirac equation
get him a new eraser.
Dirac's fascination with 'playing with i' was frowned on by my UCLA's physics experts-mentors as likely 'heading in the wrong direction' in 1974... I don't understand why these videos still appear to have a strong traction in so many 'educational settings' ...This video's minute 1:44 to 1:50 is EXTREMELY accurate!!... so why continue? (I think Spinor concepts have been deeply FLAWED for almost a century!)... This video tends to pragmatically enlighten students with flawed modern 'conventional wisdom'..This, in my opinion, is simply a 2024 analogy of a 'flat earth lecture of 1490' !!!..But as an instructor, what do you do!??!!?... Let's start exploring inversion physics! .. Oh, by the way, Edward Teller tended to agree with me in 1975!...(But, you are unquestionably a talented professor... so, please don't be bashful)...
Second
easy
Third
No
Sixth
First!!
🫡
بهتر بود جای این همه معادله خرید یک تخته پاک کن رو به خاطر میسپردی
it's so dusty😅
Well... I could understand nothing... but I think its all correct ...😵💫 but he prob. do not know what i know ant that is... cucumbers and carrots are not growing on a tree🥴
.....where the fuck did the numbers go HAHAHAHA
MIT can't afford smudgeless chalk?
physics is not playing with mathematics.....
It is.
I mean do you think this professor is doing that
“No! You can’t just define units so that c=hbar=1!”
The whole Quantum physics seems like a crap. I don't buy all these nonsense.
Clearly you don't understand it then. Understand it as in understand the math. We know quantum theory is somewhat wrong because it doesn't describe gravity, but to say it's crap is very narrow minded.
Silly. So old school
The answer is : the difference of negative & positive output power of magnetism 🧲 on the time & place 👋 ying&yang