But why wavefunctions? A practical approach to quantum mechanics
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- เผยแพร่เมื่อ 4 มิ.ย. 2024
- Discover how the behavior of a quantum particle is described by its wavefunction! 📝 Get the notes for free here: courses.physicswithelliot.com...
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📖 Summary:
Quantum mechanics deals with the laws of physics on the smallest scales. And tiny particles like electrons don't behave at all the way we're used to in classical mechanics. Instead of following a well-defined trajectory, a quantum particle is described by a wavefunction that's spread out through space, and that evolves over time.
In this video, we'll discover why we need wavefunctions to describe quantum mechanical particles by investigating a classic experiment called the double-slit experiment. The results will reveal that quantum particles share properties of both classical particles and classical waves---what's sometimes called "wave-particle duality."
It's all very counterintuitive. But the math that's involved is actually very simple! And the consequences of the experiment will lead us directly to the idea of the wavefunction.
Double-slit laser interference pattern:
en.wikipedia.org/wiki/Double-...
Electron interference pattern:
www.hitachi.com/rd/research/m...
0:00 Introduction
3:39 Classical particles
5:01 Classical waves
13:35 Quantum particles
17:47 Wave-particle duality
19:04 The wavefunction
20:47 Summary
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About me:
I’m Dr. Elliot Schneider. I love physics, and I want to help others learn (and learn to love) physics, too. Whether you’re a beginner just starting out with your physics studies, a more advanced student, or a lifelong learner, I hope you’ll find resources here that enable you to deepen your understanding of the laws of nature. For more cool physics stuff, visit me at www.physicswithelliot.com. - วิทยาศาสตร์และเทคโนโลยี
Yooo the King of Physics education has returned!
Thanks Anakin!!
@@PhysicswithElliotCould you please explain why the curl of an electric field due to a dipole is zero even though the field lines bend?
i'm honestly thanking you from the bottom of my heart elliot. just got an excellence scholarship for my first choice uni studying physics, wouldn't have had the guts to choose physics over engineering without your videos specifically. science communication is amazing and you are one of the best people that do it. so thanks. :)
Thank you! So glad to have helped :)
I am really happy for you. I chose engineering over physics many years ago and although I am happy with my career, I would’ve loved to be a physicist. Now I am 52 and living vicariously through these videos.
Elliot you deserve a billion subscribers ! Truly .. the ultimate teacher and the ultimate pure Physics content creator. No BS ! Such a fan of yours . Keep up the good work
Beautiful. Finally Physics got its 3B1B . Fantabulous. Kudos From A Theoretical Physicist. By the by, I've downloaded your dissertation "Stringy ER == EPR" [Note the Double Equal Sign, I'm a born coder], hope I shall find time to read it one day. It turns out to be one of the problems I'm working on and I've my own strange theories.
Good luck with formulating your theory!
@@darkfox8101 Thanks
yes, beautiful, and it even comes without elevator music (unlike 3B1B videos) playing in the background, to distract the viewer from the content.
Elliot, you're simply the best physicis teacher I ever had !
I’m studying physics at university and still struggle with the maths for quantum, so I am very excited for this series and this was a fantastic start! Thank you!
Good luck on your studies, you’ll miss them when they’re done but happy you did them! Wonderful times to dedicate full time to learn for the joy of it.
@@LoyalZen0x For sure, its part of the reason I’m going to stay in academia once I’ve finished my masters! And thanks!
It's better to watch something like that instead: th-cam.com/video/Q2OlsMblugo/w-d-xo.html
However, all that is a bit outdated now, after Hydrodynamic Quantum Analogs are invented. It just interference of the Pilot Wave.
Best channel with proper explanation. I was sick of seeing other channels hyping every concept to philosophical level without providing basic math or explaining realistically. Thank you.
Also, when I was an undergrad we worked with the Schrodinger equation, and solved it for the hydrogen atom, which I found fascinating. But we never discussed the Fenyman approach, so I'm very anxious for your next video on that method.
Physics should be taught Feynman diagrams first, with no artificial boundary between QFT, QM and behavior at the classical limit. Schrödinger equations can come after Feynman diagram, to build quantitative skills on a conceptual foundation. It turns out that the math of Feynman diagrams, at a certain category-theoretic level of abstraction, is much simpler than the math of wave functions. See the 2017 book by Coecke and Kissinger __Picturing Quantum Processes__. Or Coecke's even simpler 2023 picture book __Quantum in Pictures__.
Feynman's approach is fine as long as you know everything, it is simply adding up all the options times their individual probabilities. Physics today has a problem: As soon as some result doesn't work out quite as expected they assume that Feynman didn't 'cover' everything and hence 'There Must Be A Fifth Force' ... what absolute bollux :-) There is a great deal wrong in the mathematical basis of Feynman's wondeful approximations, but that is not new Physics, rather an unforgivable lassisitude amongst Mathematicians. I think I am saying that if there is a God then Feynman's precocious analytical methods will be redeemed by the end of this century and a better understanding of Physics be achieved. I would say QED but non Geometor's would read that as that other farce 'Quantum Electro Dynamics' I appologise for landing on your fine post .... I just had to get it off my chest :-)
I personally feel like throwing an infinite amount of integrals as well as green's functions at undergrads as their first introduction to quantum mechanics is a little unwise. Everyone should learn about the feynmann approach but it should be reserved for a secondary or even third course. The intuitive part is pretty pedagogical though :)
Great video. Looking forward to the those coming next. Would like to add for those that are interested in the equations that h-bar isn't technically just Planck's constant but the reduced Planck's constant, i.e., Planck's constant, h, divided by 2pi.
he’s back with another banger!
😁
Great visuals, and great explanation! Looking forward to the Path integral :)
I enjoy every second of this video. Absolutely brilliant!
I have just found this channel, weeks before QM exams. Your videos really helps to patch the fragments. Thank you the video!
Wonderful Elliot, thank you so much for your awesome work.
Excellent video. Very interesting, informative and worthwhile video.
Once you realize you need a mechanism for "how can the sum of two things be smaller than either of them individually" the idea of using complex numbers is utterly reasonable.
Can't wait for the next videos in this series!
Thanks John!
I think the concept of negative numbers suffices for this purpose.
@@APaleDotPositive numbers are addition, and negative numbers are subtraction. Sometimes we need something that is both and neither lol.
Complex numbers give us an operator that sort of hovers between addition and and subtraction...
@@CharlieVegas1st
I don't know if you know this, but you can in fact add two negative numbers.
@@APaleDot What I meant was adding complex numbers is sort of like adding two vectors, where phase information plays a role. If the two vectors (complex numbers) are in phase, we're adding to real numbers. If they're perfectly anti-aligned (opposite phase) this corresponds to subtraction. Any other phase orientation is like an amalgamation of addition and subtraction. It's like in between the two.
Adding two negative numbers (same phase) is adding two positive numbers and slapping a negative sign on the result.
Besides my answer was just sort of an oversimplification of why complex numbers are useful in addition and subtraction. They carry more information than merely "walk three steps right (addition), now walk 2 steps left (subtraction)". Being able to now move "up" and "down" gives us an operator that is "richer" in information.
I watch these videos to relax.
Awesome scholarship and presentation. Thanks.
A great explanatory video! Thanks a lot.
You came at a time when I needed it the most !!
One of the better vids on this topic. In particular I'm glad that you emphasised two points: 1. A quantum particle is quite a different 'thing' to a classical particle and 2. It makes no sense to think that quantum scale events / structures should be analogous to macro ensemble events / structure (i.e. the Greek atomists were wrong - but we had to start somewhere so kudos to them anyway). If educators (also on YT) went into those points more often and in more detail then all this lay confusion and quantum mysticism would fade away and people could concentrate on the more important unknowns. One thing would would make this video even better IMO - not showing quantum particles moving through space. I think that perpetuates another common misunderstanding about QM and perpetuates the outmoded notion of 'wave-particle duality' which we really need to put to bed now - it had its time.
Its the clearest explanation I have ever come across even as a physicist. Congratulations and thank you so much!!! Christian
i dont usually comment but this is probably the best channel to learn about physics!!! I hope we get more videos frequently
I had my first lecture in quantum physics today, seems they introduced the same topics that were discussed in this video. Really looking forward to your upcoming videos in the "series"!
Yes!! You're back!
No way this came out 4 days ago. It’s like perfect and I need it right now. But what a coincidence. If I needed it a week ago I wouldn’t have found this video. Thank you
Another fabulous video that clearly and succinctly examines another concept in physics. I make use of your videos often to help my studies. Congratulations!
Also completely false. There are no flying particles in quantum mechanics.
Woah, already hyped about the other videos
I was waiting for your video from long time plz make videos more frequently these are very helpful
hello doctor
ngl i think you're one of if not the best at explaining physics in youtube without shying away from the complicated spots lool
but i would like to ask ( i'm sure lots of us do ) which software you use for your animation ..... it would be great if you make a series of lessons about it loool 😁😆🔥🔥🔥
This is the best explanation of wave-particle duality I've ever come across!
There is no such thing as wave particle duality. That was already pointed out by Dirac in 1930. Some people simply haven't gotten the message, yet. ;-)
I can only imagine the effort it takes to create such intuitive animations.
Love you! I took Modern Physics last semester and didn’t understand well. Hopefully I’ll make it up and be ready for Quantum Mechanics next year!
Outstanding work
Excellent channel! Thanks!
One of the best explanations
Amount of work goes into these videos are mind boggling
extremely good job. wonderful
Babe wake up… Dr elliot just dropped a QM vid 😮
🤣
*Daddy Elliot
I've been waiting 7 months for this video. Time to get my pen and paper and study w/ glee. Thanks for the upload!
Awesome video! 😊🎉
Thank you!
I always like to think of wave-particle duality as simply that it's a wave when it's in motion, but when it hits something it becomes a particle. Almost like an explosion running backwards and forwards in time, depending on whether it's "free" or "captured".
Maybe because the energy excites/interacts with a single atom/electronic orbital in the detector?
Love from india.. your way of teaching is fantastic.
Please upload more lecture.
I can see Elliot being the true Physics 2 professor for a grneration of students that grew up on YT.
Amazing work.
Great video, will you be explaining the collapse of the wave function, and the measurement problem in subsequent videos?
Awesome. I guess the notes are still not posted on the page (or I couldn't find them)
They're posted now!
Very lucid. Great animation
Excellent!
Thanks Agustin!
Nice video! Where does the square for the intensity come from?
Great videos. You have a very clear way of explaining things,and the graphics get better all the time. I'm having problems with the NOTES though. If I print them onto paper, the font comes out so small that I can't read it. (Although I am very old!) I tried copy and paste into WORD, but the formulae just come out as "?" symbols.
Good explanation.
Hi Elliot!
Very cool!
So great… can’t thank you enough.
Thanks for the great video. I have a follow up question. I didn't catch why are the profiles at 8:47 already in a waveform? At 7:46 it seems to me like the each should be in form of a normal distribution curve.
What can I say... Suscribed!! .you need more followers. Great job man.
Excellent sir
sehr gut video freund, waiting for next video
For next videos, please talk about non-linear slits, shaped ones, like the integrated circuit designers use, to produce diffraction-limited masking correction. This is already a well known technology. Now being used for attempts at Moire pattern Qbits.
Love your videos
Excellent 👌
Thanks Mohammed!
Excellent
Very well done! (from an ancient physics major)
Thanks so much Eliot! I loved the video, and I can’t wait for the next! Also, any tips for an eighth grader to learn more about physics outside of youtube? Possibly places to volunteer or places that teach what you are doing other than universities or colleges. I’ll be honest I love watching physics videos, and the information goes straight to my head but the variables and math I haven’t learned go right over my head? Again any tips as to where I can learn this math on my own? Thanks again!
Thanks darkfox! It takes time to learn the math. Keep exploring all the concepts while you gradually learn the math you need to understand the details. Try finding a book at the right level and work through it---ideally with a friend too!
@@PhysicswithElliot Thanks again Eliot!
Your videos are great. This fuels interest even to those who avoid physics.
Could you please explain on Lagrangian concepts. When deriving conservation laws, why we we can't use Noether’s theorem for some differential equations where Lagrangian does not exist.
Did you look at the proof of Noether's theorem? Why not? :-)
@@schmetterling4477 can you share possible link? Thanks 😊
Хорошо что есть автоперевод. Очень понравилась подача
да, этот канал очень хорош
@@JacobRy согласен!
14:00
_... with a big bump in the region behind the hole._
However, there are already smaller bumps at the sides.
Thanks
Light behavior in double slit experiment is in line with reflection / refraction situation when the resulting wave is the sum of original wave plus waves produces by electrons in the medium the light is passing through.
Maybe the electrons also produce some kind of waves which "excite" the matter around them. And the observed behaviour is the sum of the original wave plus the waves from the excited matter?
Thanks for sharing this, at least for me you have the perfect speech/thought ratio to follow along. I did bring a fair bit of previous knowledge, but your pace of explanation helped to bring some more intuition into my understanding. So, thanks again, and of course: ++sub;
A tiny request to discuss mathematics behind physics like videos . Like the important part of maths with details that are required in physics. Btw this is a fantastic video ❤️❤️❤️
Awesome.
What softwares do you use to create these videos?
One more weird phenomenon he did not mention is that a detector placed at either hole, so we know which hole the electron passed through results in a pattern that looks just like the pellets. In other words, the interference pattern is gone, and the electrons act like classical particles. If we turn off the detector the interference pattern re-appears.
I would say "remove" rather than "turn off". As long as the detector is present, it will disturb the electrons enough to destroy the interference pattern.
@@gcewing I think that "turn off" is rightly formulated. We don't speak about electrical disturbances here. The fact that the detector is on and MEASURES the going through of the electron, makes the wave function "collapse" and makes the electron a particle. Turning off the detector makes measurement impossible at the slit hole, and therefore the electron can continue to behave like a wave. Greetings - Johan
Bro , I just comes to know about you bro ,And you are just insane bro ,Unbelievable bro ,Aswsome bro 🙏🏼
You teaches things so good bro , Another level bro 💯 🙏🏼
Thank you so much for giving notes for free so that A middle class student like would able to get to know about Quantum Physics
Don't leave it bro. PLEASE continue this bro until you can possible do bro
Thanks from an Indian ❤❤❤❤❤
19:55 : so interesting that in the classical wave sense you need to square the sum of functions only because we are using a math trick ( taking only the real part of complex numbers) , but in the quantum sense, nature is telling us that nature itself is using something similar to a "math trick" by squaring the sum of the quantum wave functions in order to produce "the real part" , ie, what we see. What is the interpretation of my statement? Does it have any significance, is it a coincidence, or is there some deeper meaning?
When will we get the other parts ?
When quantum particles are sent through the slits one at a time, does the time between electrons have any effect on the outcome (besides it taking longer for the pattern to emerge)?
Not due to the reason you are suspecting. Electrons are not a good system to test that, though. Light is a much, much better one. In the optical double slit the intensity of the light doesn't matter at all (assuming that it's not so intense that it destroys the matter the apertures are made of, of course).
I am more interested in how do you make such smooth animation 😊
Is the wave function the attempt to locate a particle in the future (Quantum Mechanics) and a particle when it can be observed in the present/ past (Classical Physics)?
A+ on the vid. content
5:40 Single slit also generates interference pattern
20:42 h-bar is the reduced Planck constant? 🤔🤔🤔 it is equal to h/2*pi
hbar is almost always used rather than h in physics, so we just call it Planck's constant
brillant👍
your the reason i can do most things in physics
Thank you very much, this video is brilliant and explains it very well especially for a non physicist like me. However I do have some questions, lets say an electron behave as a particle wave, and the base ball behaves as a particles but at which scale does this transition in the behavior happen, does a simple hydrogen atom with one proton and electron behave the same, what about a bromine atom with 35 electrons, what if it is a macromolecule? 🤔
Then you are simply telling us that you didn't pay attention in high school where we are teaching you that "a quantum" is a small mount of energy. It's not a wave and it's not a particle. ;-)
This is good, but I think it's important to stress that the wavefunction is - must be - more than just a probability distribution. It's irresistible, especially for beginners, to think the wavefunction could just be a probabilistic representation of our knowledge of the particle, where the particle goes on 1 path but follows some complicated rule we don't know about. This _cannot_ be the case, because of statistical impossibilities in certain experiments. I know you know this; I just think it should be stressed more.
Someday I will hopefully make a video about Bell's theorem!
It also should be remembered that there is deep necessity for the wave function to be complex valued. But explaining this without advanced maths is really not straightforward. Also it really is a probability amplitude distribution.
That’s not a consensus opinion in the physics community. Sometimes taking the math too seriously, and ascribing to it too deeply an ontological significance can be just as problematic as not taking it seriously enough. Bell’s theorem has quite a few holes one can poke in it, philosophically speaking, if that’s the matter you’re referring to.
The particle goes through one slit, when it pilot wave goes through both slits. What is the problem?
@@VolodymyrLisivka The same (main) problem that any "classical model of quantum mechanics"* has, namely "nonlocality" or "spooky action at a distance". Pilot Waves has other conceptual and technical problems peculiar to itself but one should be careful before pursuing _any_ such proposed alternative to quantum mechanics. There are people who have retained a commitment to "classicality" or "Realism_2" [ DOI: 10.1088/1751-8113/47/42/424011 ] despite having acquired a full and up to date understanding of the conceptual and mathematical issues (e.g. the well known quantum foundations researchers Matt Leifer and Matt Pusey) so it's not an _intrinsically_ unrespectable position.
* Landsman's more apt term for a "hidden variable theory" such as Pilot Waves / Bohmian Mechanics. DOI: 10.1007/978-3-319-51777-3_6
I finished an ODE course and learned much about Laplace transform, but I no longer have any math courses in my engineering degree plan. I noticed a load of connections with these ideas and those of waves, signals, and electrical concepts. I am enrolled in a Petroleum Engineering program btw so I’m not sure if I will be able to use mathematics much further than ODES, but I would love to if possible! I would like to learn more and potentially undertake a Masters in something that might be similar to Electrical, Quantum, or even Nuclear!
The other day, I watched an interesting video which described how an MRI machine works and it brought up Fourier Transform! Anyways, I was wondering, what is the purpose of PDES, Fourier transform, and Z transform? What about the complex world? (These are some things I haven’t covered much). Also where might I see such things pop up?
Also there is one last topic I would like to bring up, which is only tangentially related: Careers. I have about 2 more years until I graduate with my Bachelors degree. Is there anyone who can maybe give some advice on what path to take or maybe something I should absolutely involve myself in in order to launch my career? I was thinking of applying to several co-ops as well as internships, but I also noticed that it is possible to join undergrad research opportunities. Anyways there was a lot I wanted to say and it was rather disorganized, but for anyone studying engineering right now, I wish you the best! You got this!
Also Physics Majors are true Chads
When they describe the wave function, isn’t it more of a wave pulse, and not a periodic wave? When you fire one electron at a time at the two open slits, the electron appears in some location on the back wall in a “building wave interference pattern”……how is momentum conserved in the one electron case?
Every time you explain, I actually understand 😂
In the case of the BBs, the highest hit-rate is dead center? Between the two slits? Whatever happened to 2 clumps?
The two single-slit curves wouldn't combine in the way shown in the animation, having one high point.....there would be two high points
Hey elliot had a problem,
I am a young guy interested in teaching physics further in my life but don't wanna do it the traditional way, is the TH-cam way practical?
BTW love the work you do
What do you think? Can you learn to play American football on TH-cam or do you have to go on a field and learn to throw the ball? How about the piano? Can you learn the piano without practicing? OK... so why in the world do you think that you can learn physics from videos? ;-)
Bravo
Thanks mikip!
There can be some more to add to this issue. Let's say that we have two slits but we make one infinitely large and then pass photons through them. Phi (r1, t) would not be symetrical to the phi (r2,t) of the vertical coordinate y as a f(t). Also, it is hard to understand this phenomena even in classical manner where x is f(t) but if you consider inverse function such as as t(x) then symetry gets lost again because we don't have the definition of time. Also, this implies that all this stuff was not discovered but invented something like Richadr Feynman did.
some thougths would actually now flood my mind on what is the cradle of all being and any given entity since I have just listen to Tarjas < bless the child > and there the line < think of me long enough to make a memory > got me this way, as the AP's in the cerebrum to create a memory are pure electromagnetic energy, but due to sombre asymmetrics I cannot but want nonetheless place the fragments here, so as to being able to pick 'em up later, when I am done with what needs to be pulled off first...
...might it be that the quantum field of the photons is somewhat very fundamental to all other field regulations? and here is why this crossed my mind... ...in the beta-decay you end up with an electron ( and a neutrino of course... ) where you wouldn't expect an electron to emerge since the neutron that surpasses a metamorphosis to a proton is totally hadronic with two down quarks and one up quark and therefore nonleptonic and nonetheless there must be interactions with the field of the photons to have these electrons emerge in that photons are emitted by the electrons and need to be as for me their fundamental base rather than some additional feature and furthermore is gamma ray able to let electrons emerge ( gamma ray is actually photonic... ) on collision with molecules with positrons that emerge also and that bears the question which way the field theory must be entangled in the theory of anti-matter, where it is clear - as it would contradict the uncertainty principle after Heisenberg - that fields must exist without the possibility thus of absolut empty space ( I think of it as the mark of God... ) in that this would require the field strength to be zero as the differentiation in function of the time would need to be likewise zero... ...and that isn't possible according to the Heisenberg uncertainty principle that not only refers to the momentum and the locality of a particle... ...so the field of the photons may be very fundamental to all other fields and the fields themself the way they get excited may provide some answers to what ends up being antimatter and what ends up being normal fermionc matter... ...and isn't it interesting speaking of a fundamentality of the photons to keep in mind that positrons likewise electrons do emit photons thus photonicity may very well constiute a base of all that is?
Le p'tit Daniel
Wow 🎉🎉🎉
Is it correct / fair to say that this isn't mysterious anymore if you consider the electron as something big enough that it does go through both holes?
Not mentioned in the video. The slits need to be comparable in size to the wavelength of the light which needs to be also monochromatic.
The probability (wave determining) the pattern the photons will create does not require time as a variable. So, of course you expect the patterns shown in all cases based on wave mechanics. Time is not a QM variable. I don't understand why people have such a hard time with QM.
In this speculative scenario, let's consider Leibniz's Monad, from the philosophical work "The Monadology", as an abstract representation of the zero-dimensional space that binds quarks together with the Strong Nuclear Force:
1) Indivisibility and Unity: Monads, as indivisible entities, mirror the nature of quarks, which are deemed elementary and indivisible particles in our theoretical context. Just as monads possess unity and indivisibility, quarks are unified in their interactions through the Strong Nuclear Force.
2) Interconnectedness: In the Monadology, monads are interconnected in a vast network. In a parallel manner, the interconnectedness of quarks through the strong force could be metaphorically represented by the interplay of monads, forming a web that holds particles together.
3) Inherent Properties: Just as monads possess inherent perceptions and appetitions, quarks could be thought of as having intrinsic properties like color charge, reflecting the inherent qualities of monads and influencing their interactions.
4) Harmony: The concept of monads contributing to universal harmony resonates with the idea that the Strong Nuclear Force maintains harmony within atomic nuclei by counteracting the electromagnetic repulsion between protons, allowing for the stability of matter.
5) Pre-established Harmony: Monads' pre-established harmony aligns with the idea that the strong force was pre-designed to ensure stable interactions among quarks, orchestrating their behavior in a way that parallels the harmony envisaged by Leibniz.
6) Non-Mechanical Interaction: Monads interact non-mechanically, mirroring the non-mechanical interactions of quarks through gluon exchange. This connection might be seen as a metaphorical reflection of the intricacies of quark-gluon dynamics.
7) Holism: The holistic perspective of monads could symbolize how quarks, like the monads' interconnections, contribute holistically to the structure and behavior of particles through the strong force interactions.
If screen is displaced consider all cases in obsevation for n sources
How far apart in time must one go before individual electrons do not build up an interference pattern? I guess proportional to the distance between slots and screen? If more than the time it takes for a particle to traverse the whole distance from source to screen? What if several seconds, or minutes or hours? well, I'm struggling with that. Thoughts?
Individual electrons never make an interference pattern. They give us a single position, if position is what we are measuring. We always need many quanta of energy (which is what we are really measuring) to build up a pattern.
@@schmetterling4477 Thankyou. Better, 'how far apart in time before single electrons do not form a distribution pattern reminiscent of interference?'
@@tim40gabby25 They always form these patters. The patterns have absolutely NOTHING to do with interactions between electrons.