What is Quantum Tunnelling?
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- เผยแพร่เมื่อ 28 ก.ย. 2024
- This video explores one of the most fascinating and esoteric properties of quantum mechanics: quantum tunnelling. The video begins by explaining an apparent paradox involving alpha decay, and then goes on to show how the theory of quantum tunnelling can provide a solution. The Schrodinger equation is solved for a rectangular barrier, and the tunnelling probability is calculated. A simplified model of quantum tunnelling is then used to calculate the half-life of Polonium-212, and the theoretically determined value is compared with the experimentally determined value.
Quantum physics of atoms, molecules, solids, nuclei and particles - Eisberg and Resnick
Introduction to Quantum Mechanics - Griffiths and Schroeter
Introductory Nuclear Physics - Krane
Vibrations and Waves - King
HyperPhysics Tunnelling example - hyperphysics.ph...
The Quantum Story - Jim Baggot
Quantum Physics for Dummies - Steven Holzner
Thirty Years that Shook Physics - Gamow
Inward Bound - Abraham Pais
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Compared to the pop sci channels, this feels like physics for big kids
For anyone who has taken college level or IB level chemistry and/or physics 101
@@SolidSiren
I’m an autodidact & incur little difficulty.
@@nyrdybyrd1702 Electrical engineer here who got his degree 10 years ago. I can follow the principles with not to much difficulty, but my math skills have become really, really rusty. What I use everyday is quite basic, except for the use of complex numbers as a convinient way of dealing with phase angles and the occasional differential or integral.
Yes, used a lot of it during university, but weaseled myself around the heavy parts and now somewhat regret that.
@@VintageTechFan I think my brains might be all over the walls when quantum comes up...
@@nyrdybyrd1702 autistic adhd ocd dl autotelic autodidact debutante here.
Nontraditional "learning" is my jam, however
my prefrontal cortex is a unicycle and the devil rides the pedals. I go where the flow takes me, no power steering. 🥸
This channel is one of the best on youtube, PE is going to the effort of creating a presentable explanation of things that most people learn and move on with. PE, your videos are a gift to the internet, thank you.
That is very kind of you to say, thank you!
@@PhysicsExplainedVideos I listened very carefully to this explanation and think I followed it reasonably well. I do have certain uneasy and misgivings about what I heard which may be you could consider. Firstly if your stating point is a theory summarized in an equation the solution to which is a probability density for position (and that equation can be solved everywhere) then even before you start you know that there will be a solution that shows the particle on both sides of the barrier. So in a sense the result was baked into the theory a priori.
My second point concerns what I think you called the reflection coefficient. This is defined as the ratio of the modulus of the coefficients of the travelling wave solution on the left and right hand side of the barrier. Well I can sort of grasp that but it does have rather the feel of a recipe . For example the travelling wave in the well supposedly representing travelling in the opposite direction was excluded. I can sort of see this but again it has the feel of a recipe based on thinking 'classically'.
My final point is that a lot of the analysis did rather depend on thinking classically. For example the particle was looked at rather as a ball rattling round in a sphere that could only penetrate the barrier when the particle strikes the 'wall'.
Don't get me wrong I was pleased to see this explanation. However, it just looked a bit too add hoc. On the other hand I have no idea how it might be done otherwise.
Well there is one explanation why a U238 atom can emit a alpha when the energy level is too low to eject the alpha: The energy of the alpha emission of U238 is higher than 4.267 but some of the energy is lost as the alpha partial exits the nucleus. For instance imagine a bullet passing through a barrier. Depending on the barrier resistance, the potential energy of the bullet will be considerable less as it exits the barrier. If a bullet energy drops below the level need to exit a second barrier, it does not mean it didn't originally have enough energy to pass through the first barrier.
We could presume when the alpha ejected from a U238 atom has ~8 MeV but losses half of its energy exiting the barrier.
The issue with the mathematical derived estimate of the half-life of Po212, only assumes a single atom. In a mass that consist of a large number of atoms would be distorted considering that the mass or number of atoms part of a mass influence the number of alpha emissions in a give period. The model used in this video does not reflect the external influence the rate of emissions based upon the mass. Its based upon a single atom the estimated number of collisions per second on the barrier.
@@PhysicsExplainedVideos Integration is dual to differentiation.
"An infinite number of infinitesimals" -- barrier potentials are equivalent or dual to each other.
Treating each infinitesimal equally conforms to a principle of objective democracy!
@@guytech7310 dude why are you trying to debate the process of the video? He literally says in every video that he’s just following the path of the people who originally derived the answers. He’s not pulling these explanations, examples, and experiments out of his ass, he’s just presenting how it was originally done by the people who did it.
Superb explanation with just enough detail to see how the ideas actually connect together. I love the level of rigour and the fact that you do not shy away from showing the mathematical magic that is operating behind the scenes! Great work!
Thanks for the kind words! Much appreciated
@@PhysicsExplainedVideos For some reason this seams to be stuck in my mind and I keep thinking about it. A bit of a snag occurred to me when I realized that the wave function was not normalizable. I guess this must be why the reflection coefficient is defined as it is. It would not be possible to integrate the wave function over region 3 which I would be tempted to do to find the probability of finding a particle on the other side of the potential barrier.
More than two decades ago, I used to get lost in physics books. It gave me great joy to study and imagine. Watching your videos (which I have just discovered tonight) is bringing me that same joy. I feel like I am 16 again :)
Awesome video! I especially liked the little calculus lesson at the end. I'm so glad to have found a physics channel that goes beyond pop sci for those of us with STEM backgrounds but are not necessarily physicists. I really appreciate the work you put into your videos!
Remarkable work from one of the most underrated physics channels on youtube 👏👏
Thank you! Very kind of you to say
24:12 For anyone wondering, the way this is done is by solving for B in 1st equation: B = -A +F +G, then plugging -A +F +G into the 2nd eq in place of B. Similarly, to combine the next 2 equations (24:19), to relate C and F solve for Ge^βa in first equation: Ge^βa = Ce^ika -Fe-^βa. Plug in to 2nd equation ---> -βFe^-βa +β(Ce^ika -Fe-^βa) = ikCe^ika ---> 2βFe^-βa = (β-ik)Ce^ika. Relating G and F is a little easier as Ce^ika is already directly solved for in terms of F and G in the first equation, so just plug that into 2nd equation.
thank you, very helpful
Theoretical physicist here. Very nicely put together! I would've added some justification for the wave-function not being complex valued inside the V potential.
Thanks for the feedback, yes, I think that would have helped!
Simply superb. Your videos glue me to the topic from start to end and I confess that were these videos available during my physics graduation time ( 80s decade) , I would have perused to higher levels of physics academics.
You're very welcome!
You need to get a Nobel Prize for explaining things others thought they knew and actually got a PhD on - not knowing like you know.
Great video and brilliant lecturing. Only one thing. While QM and tunnelling is useful and correct in explaining this problem, we shouldn't make it appear that it is the only way to explain the problem. This is not different than the problem of evaporation. Molecules can evaporate from the surface of a liquid even at very low temperatures as they acquire enough energy. The energies of the molecules is a range not a single energy due to motion and continuous interactions. Those who are more energetic escape first. regards.
PE is simply the best physics channel on TH-cam!
That was one of the best videos I've ever seen. It's fantastic. Congratulations on the scientific rigor👏
Glad you enjoyed it!
Sir you are great 👏👏👏 🥳🥳
I really appreciate your work
Keep making such videos
I have not find such type of great content on internet as you providing us.
God bless you sir ❤🥰
Thank you so much 😀
Thank you for not trying to dumb this down and stuck to hard physics 👏
I repeated the same calculations, to see whether more iterations made a big difference.
I use these values: 1MeV= 1.602E-13J, hbar=1.05457E-34 Js, m=6.644E-27 kg.
At x=9.01 fm I replicate β = √(2m(V-E))/hbar = 1.826E15 m^-1.
For the crude approximation (block-shaped potential), using an unrounded value a = 17.89 And T=e^(-2βa) and f=1.14E21 Hz, I get a halflife of ln(2)/(fT) = T_half = 1.44E7 s
Dividing up and using the middle of each part, like in the video, I get the following half lives.
With 5 steps: 240 ns, 50 steps: 229 ns, 500 steps: 228 ns. So it seems to converge well, and 5 steps wasn't all that bad
A different issue is the prefactor 16E(V0-E)/V0². It was polished away because it had order 1, and later the result is 'pretty close'..? Maybe it was also an inconvenient factor?
If I bring it back in, it makes a lot of difference (for the block potential I now get T=4E6s)
and, what is the rationale, when combining n steps, such a prefactor goes to the n-th power!??
As someone that is learning math and phsisyc on youtube. You provide me the knowledge that anyone is uploading. So gracias por tanto y suludos from Bolivia
Happy to help!
I love this channel.
It's refreshing what I learned & it's increasing my knowledge.
Thank you for this.
I absolutely have no idea what you're talking about.
But the idea that people want to know how the sub atomic world works and tell the story via mathematics is fascination.
Great video
I absolutely love your videos. While I became fascinated with physics again by watching Sean Carroll's "Biggest Ideas" series, I gotta say, you take the cake in my book. In my opinion, your explanations are right up there with 3Blue1Brown's for math (although, you did also touch on Riemann way back, which was actually how I found you strangely enough).
In particular, watching your previous video was when it finally clicked for me why complex numbers must be included in all things quantum. Additionally, this has been by far the best video I've watched on quantum tunneling.
However, some constructive criticism: In both this, and the previous, you power through some differential equations like its nothing. That's fine by me; I'm very rusty from school, but I can remember just enough to follow the gist of your steps. But yet, at the end here, you go through all the painful steps before getting to the integration?
My recommendation would've been to go straight from the uniform potential calculation where things go horribly wrong (important to show there is such a thing as oversimplification) to the integral of the actual curve. Just my two cents though.
All in all, fantastic vid though. Keep up the great content!
Amazing content 👌
It helps a lot to watch Steve Brunton's lectures on solving ordinary differential equations, before watching this, it did for me at least.
This a phantastic presentation, actually very effective teaching, thank you!
These recent quantum mechanics videos have been amazing (really your whole channel is fantastic) - thank you!! I'm looking forward to the video regarding neutrinos you mentioned!
This channel is prob the best recommendation in the last few months.... great content!
Glad you enjoy it!
Sublime! Thank you for your incredible education to the community. As an EE, you're making me wish I pursued theoretical physics instead..
Thank you very much, your channel is a treasure.
i'm really thankful please keep it up!
Glad you enjoy it!
Great job! Look forward when you decide to tackle the topic of Bell's Theorem.
Great suggestion!
i dont know why but i got this topic as intruductry part syllabus in my grad. This video actually developed my intrest in Quantum physics
It was heartbreaking to get the disgusting result at 35:03 But seeing the accurate result pop out later with the new model was super climactic and satisfying. I thought that a changing potential barrier would require some high-tech mathematics to work with, but how it can be modeled in such a genius way of "succesive tunnelings" is amazing.
What happened to the uncertainty principle video?? I was halfway through watching, came back today and it's gone!
This is the best explanation for tunneling I've seen! Thank you so much!!
Glad it was helpful!
You're a good teacher! Very clear words and presentation, and I love your 'very british'!
Congrats on 200k man
One of the best physics theory i have learned in my life.
Glad you think so!
This was like diving into pool intending to touch the bottom, only to find you are in the Mariana trench
I'm not even sure I can get back to the surface from here!
Quantum physics describes phenomena which in earlier centuries were considered miraculous. The tunneling of particles through inpenetrable barriers. The transmutation of chemical elements. The entanglement of distant particles (spooky action at a distance). Quantum physics overthrows our notions of locality and reality. The more we learn about reality, the stranger it appears.
This is a great explanation, well done!
Thanks!
Im dumb and have absolutely no knowledge about or use for any of this info. However I have fallen asleep to this video six times now. Excellent video.
Can you make a video on defining time and space?
This makes me think about how we are walking on the shoulders of those before us. We have our comfort and safety to literally millions and millions of people learning about our surroundings and how to use that knowledge to build upon to make bigger discoveries... I feel privileged to have been born in the time I have... To be honest and now that I know better I'm REALLY glad I wasn't born in like the year 1105.. YIKES... I like my comfy jammies, warm showers and morning coffee WAY too much to now NOT have it.. lol.
Great Compilation! Very informative:-)
However, In the slide showing tunneling probability in different regions , Region 3 showing "after tunneling" probability should not have been a flat exponentially decaying line but a sinusoid(^2) with same wavelength as the sinusoid (^2) in Region 1 "before tunneling" as the momentum (& Kinetic energy) don't change during tunneling, but much smaller yet constant amplitude in region 3 as tunneling probability is much lower. The exponential decay part applies to only Region 2.
The graph doesn't show the wave function itself.
Quoting the author: "The wavefunction in region three has the form Psi(x,t)=Ce^i(kx-Et/hbar) which has the form of a plane wave"
So the wavefunction is still a wave, but the probability density is a constant.
I would like to tell you that your channel is the best channel that I have ever found on TH-cam. Your way of explaining physics is awesome, it is accessible to every one once they know how to resolve differential equation and, in my opinion, that is how we should learn physics at school and I am sure that plenty of students would have understand advance physics. Thank you for providing us all that knowledge. God damn it, now we can find mathematically the all life of an elements, it is awesome!
Ps: Are you planning a video about the lagrangian equations or the repartition of the speed of particle in a gas in thermal equilibrium ? ( I know, it is two very different topics but I just want to know😅)
Or a video about the general relativity ?
MARVELOUS EXPLANATION, CLEAR AND TO THE POINT
Excellent video and series Mr. Physics Explained. I assume you are not Brian Cox, even though you sound like him in your voice inflections and intonations, and have his knowledge of physics and joy in communicating it. You know Dr. Cox by any chance?
Really well done as always. I think this one could have used a bit more simple explanation of what physical process this math is explaining, in layman's terms if at all possible - I am not sure what all the abstractions are meant to represent despite being able to understand where the math is coming from and how it fits together. For example, "hits the barrier" - I don't know what this is meant to mean in reality. What barrier? Where are the alpha particles coming from? A bit more groundwork in the physical processes the math describes would be nice. Thanks!
please come back 😢 we need more videos
Exactly what i was looking for!!
Excellent video! What was Gamow's justification for approximating the internal oscillation frequency based on a single alpha particle though? E.g. Uranium 238 with 92 protons arguably comprises "46 alpha particles" + 54 neutrons, so presumably there's some statistical energy distribution argument that justifies modelling the frequency as a single one of those?
Congratulations! Now you have one more subscribed! Most of YT channels in Brazil are pretty much arrogant in terms of saying how the things are in Physics. It is frequent to find vídeos titles as "Quantum Mechanics Explained" or "Relativity Theory Explained", among many others. Even Richard Feynman refused to state that he understood It well or he had any idea why QM made sense as a science. But in Brazilians videos you see and hear only bla bla bla, and not a single explanation is given. I never see in Brazilian videos Schroedinger Equation being writen before. You wrote It and solved It to the specific case of finite step potential to use the result in Alpha particle paradox explanation. I tell to Brazilian TH-camrs: "ok explain us what is Quantum Mechanics, publish your conclusions and go to Stockholm to get your prize!". I never get echoes from my questions. At the end ALL these Brazilians TH-camrs science guys have no background in science, some of them have milions of subscribed viewers. They are only papagaios (Brazilian birds that repeat words spoken to them - parrot birds in English, I guess) and their viewers are parrot cubs.
Nice video.
The sad thing is, that many people confuse mathematical models with reality and consider those be an explanation for anything - which would only be true if we were living in a simulation.
And do not forget to include space weather (solar wind, cosmic rays etc.) in your models of earth and it's climate.
Excellent explanation on the quantum tunneling. Just one question, the quantum tunneling probablity was estimated with the assumption that Gap ''a'' is a very wide gap, I understand the assumption as it allows for easy calculation. But when we divided the gap into infinitesimally small gaps, would the assumption of wide gap not break down? But even then the alpha decay seems to correspond incredibly well with the experimentally determined values. Why ?
Can you also explain, how this quantum tunneling was used to create a microscope that can give you atomic scale visualizations?
Please sir upload all the videos of quantum physics for Bsc students.Your videos are exceptional.
The ending was beautiful .
Thank you for making this video!
pure gold .. thanks for the service..
Glad you enjoyed it!
University A tunnel diode or Esaki diode laboratory experiment, in this video barrier shown simply as rectangular not fancy integral inside exponential. Nice job. Final result is not so important but logic and rationality of process that is beautiful.
Is very rare that you can find and numerical example, theoretical physics thinks that they discovered new law in form of equation, experiments and numerical example is not their job :)
I’ve been putting this video off for a while because I have a feeling I’m not ready to understand it. But I just can’t help myself anymore. Let’s go!
As a retired chemist I love this channel
Hi, i hope you see this comment, i just wanted to request to if possible can you make a video showing the exact mathematical derivation of the Dirac equation.
Because it combines lorentz invariance with quantum mechanics and spits out the Existence of antimatter along with explaining quantum spin.
Based on your previous videos and this new Dirac equation video, it would very possible to set an mathematically rigorous foundation to build and understand the concepts of quantum field theory.
Thanks
I am working on a Dirac Equation video, hopefully should come out in the next couple of months
I would love to see you do one on the mathematical discovery of the positron…still blows my mind that it was just hiding in the math. Plato and Aristotle would still be at odds today. ;-)
Coming soon!
Thanks for your videos! Really enjoying them.
One thing on quantum tunneling, not sure I follow. When Alpha particle emitted from atom, it seems should tunnel atom forces (strong forces I think they referred to?) well. Not sure why it is Coulomb well.
Please make a video on the mathamatical existence of heisenberg uncertainity principle ...
My next video should hopefully address this :-)
There is a language problem with your electric potential energy formula due to the ambiguity of the denotation V, which can be interpreted as voltage or electric potential difference. The formula of voltage of any particle in the electric field of any other charged particle is V= K Q/r = = Q1/ 4πεr, and electrostatic potential energy for a 2 particle system is Q1Q2/ 4πεr. The only difference between the different formulas is Q2
Will you be making more videos next year? Also, Happy New Year's @PhysicsExplainedVideos
It's amazing we discovered radiation. I could see us learning about heat IR radiation. But. Radioactive material that emits invisible particles is just facinating that we discovered that.
Great lesson!
Haroun Katchi
It is amazing that the half live estimate at 34:49 is 14 orders of magnitude too high, whereas the approximation of the barrier as a rectangle instead of a part of a hyperbola is probably within one order of magnitude. Taking 5 intervals then would not be a good basis for expecting accurate results, imho, but it is good to see the improvement it does!
Another point that I have, was the nucleus at the time modeled as a hollow sphere in an α could move freely without any force acting on it? And why did they assume V=0 inside?
Very good explanation. Excellent job.
I just love how the solution is simply to allow the partition to be made finer and finer, calculus style.
-29:36 The existence of imbedded Helium atoms or just Helium nuclei, inside the electron 'layers' ( lack of a better word for shells) of the Uranium atom is astounding, but understandable.
Excellent video. Thank you for making it 👌
Glad you liked it!
6:13 The gamma ray can be associated with electron capture. The element does change.
That's was just mind blowing
Excellent explanation! The end justifies the means :) ?
Indeed!
What happened to the Heisenberg uncertainty video it was very good.
You are making very good and understandable videos hope you soon join the league of other science educators
at 37:00, is it not just confirmation bias? because the frequency of collision inside the nucleus assumes that it moves freely through the nucleus which it clearly should not and at that energy, you‘d possibly even have to consider relativity. And also the barrier‘s end can be rationalized but ut doesn‘t change that it is somewhat arbitrarily chosen.
Great video either way, very interesting and I did learn quite a bit but the result gotten from the last calculation feels impossibly close
Wasn't it here yesterday? Like 2 times? I guess there is some correction - could I get TL;DR what is correction? Because I have your video fresh in mind.
I also thought I had deja vu
a double deja vu - maybe i watch it to finish next week, when there is a fresh premiere 😎
it was there yesterday but he privated that video
Same
He might be doing a diagnostic trial to see if frequent posting gets more attention.
Can you please make a video about Einstein’s field equations? 🙏🏼
Love your amazing work !
Thank you so much!
Dude your channel is amazing. Not sure if you’re still making content, but do you know anything about scalars?
Scalars are just objects (usually the real or complex numbers) that you multiply something by to "scale" it.
If v is a vector we can have the expression w=2v and there 2 is a scalar.
For general math topics I recommend 3blue1brown on TH-cam.
@@narfwhals7843 3blue1brown is great, but I'm not interested in general math topics. Perhaps I should have been more specific. Can OP do a video on the scalar-tensor theory of gravity? (or even a comment to reply would be great!)
@@robertmcknightmusic ah, well that's a _much_ more complicated topic than just scalars 😅
The problem I had when I learn physics is that... everything is so hand wavy without a quick summery of the non-hand wavy solution. For instance, why can we naively get the attempt frequency by E=1/2 mv^2? why can the eigen state solution be interpret as tunneling coefficient? Why do those semi-classical heuristics even work at all? It's very useful to learn the hand-wavy heuristic in solving the problem, but I think it's also at least interesting to give the audience an idea what the proper solution look like without showing it in its full glory.
When the new video man we need moreeeeee
Heyyyy..... another video
Thank you
No worries!
i just love this channel ♥♥♥♥♥♥♥
Could u do a video on general relativity plz😊
can you do a vedio abt statical mechanics
That's what this math describes.
Is spontaneous fission of nuclei heavier than thorium explained in the same manner?
Schrödinger equation very hard to understand 😊🎉
What happened to the uncertainty principle video? I was going to watch and study today 😔
Doesn't this mean that all nuclei will have some(however small) probability of alpha decay?
You could try to repeat the calculation for different nuclei, and see if the predicted decay time matches up to measurement (which can range from microseconds to years or more, depending on the atomic species!).
Please upload more ♥️♥️
Dumb question, but is the barrier the alpha particle has to overcome the strong force?
Please do Maxwell's Equation please
Whenever I feel like I’m being denied the full story because of the math, I come here to be reminded why.
Fascinating
Why does the alpha term disappear in the integral?
Quantum tunneling is the perfect example of folks just making stuff up, as needed.
lollll
Please sir, I want some more...with bowl in hand.
Thanks!