What is Quantum Tunnelling?

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.phy-astr.gsu.edu/...
The Quantum Story - Jim Baggot
Quantum Physics for Dummies - Steven Holzner
Thirty Years that Shook Physics - Gamow
Inward Bound - Abraham Pais
You can help support this channel via the Physics Explained Patreon account: / physicsexplained
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You can follow me on Twitter: / physicsexplain1

[@jameslockwood8008]

Compared to the pop sci channels, this feels like physics for big kids

[@SolidSiren]

For anyone who has taken college level or IB level chemistry and/or physics 101

[@nyrdybyrd1702]

@@SolidSiren I’m an autodidact & incur little difficulty.

[@VintageTechFan]

@@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.

[@MadScientist267]

@@VintageTechFan I think my brains might be all over the walls when quantum comes up...

[@theWinterWalker]

@@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. 🥸

[@kieranhosty]

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.

[@PhysicsExplainedVideos]

That is very kind of you to say, thank you!

[@tomasstride9590]

@@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.

[@guytech7310]

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.

[@hyperduality2838]

@@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!

[@ghostprime6320]

@@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.

[@stevecraig2060]

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!

[@PhysicsExplainedVideos]

Thanks for the kind words! Much appreciated

[@tomasstride9590]

@@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.

[@samw3086]

I liked your approach to solving complex physics problems (and equations) and reducing them to something engineers will understand and use day to day. The discretisation of the tunnelling width was the key concept here. Going to the full integral fixed a 13% error in the result but would have detracted from the explanation and solvability of the problem for a lay person. The 5 element model was indeed credible with respect to the measured results. Bravo!

[@PhysicsExplainedVideos]

Thanks for the comment!

[@thegreatveil5699]

An outstanding introduction to what I consider to be one of the greatest breakthroughs of XXth century physics. The concepts behind quantum tunneling migrated almost immediately after Gamow's work to condensed matter physics, where they set the foundations for the quantum theory of electronic transport, ultimately culminating with the development of the transistor and semiconductor electronics which have shaped today's society. Gamow himself is one of the most fascinating personalities of XXth century physics. He glimpsed everything, from the structure of the atomic nucleus to the idea of a dynamical Universe beginning with a Big Bang. He predicted quite accurately the temperature for the afterglow of such a Big Bang about a decade prior to its accidental discovery by Wilson & Penzias. With the host's permission, I will leave a few words regarding the modern field of alpha-decay, which readers may perhaps find interesting: In 1929, Rosenblum measured the lengths of alpha tracks in a cloud chamber and discovered that they were unequal. Alpha particles were in fact radiated in groups of closely bunched, but unequal energies. This was one of the first forms of experimental evidence suggesting that atomic nuclei have an internal structure, in a time when the neutron was still undiscovered and practically nothing was known about what really happened inside a nucleus. Today we know that nuclei radiate spectra of alpha particles, the various lines in a spectrum corresponding to transitions leading to excited states of the daughter nuclei which decay further to the ground state through gamma cascades. Thus, nuclear spectroscopy is a very intricate field, where the dynamics is driven both by electromagnetic and nuclear interactions. In opposition to conventional wisdom, alpha particles do not in fact exist "inside" nuclei. A more accurate picture would be the one where they spontaneously emerge on the nuclear surface and dissolve back into the sea of nucleons, with only a small probability of escape being given by their quantum nature and the mechanism described by our host. The reason for their dissolution lies in the sharp increase in nucleonic density as one dives deep inside the nucleus. This medium of strong interactions breaks the four-particle correlations that make an alpha-particle a bound object, essentially dissolving it. Such a picture is suggested by calculations done in infinite nuclear matter, where a transition from a phase of nucleonic matter to one of alpha-particles takes place only at low densities, but performing the calculation in a satisfactory way on a nucleus of finite size has yet to be achieved. The exact mechanism of an alpha-particle's formation and break-up in a finite nuclear system remains the biggest mystery of the phenomenon and the only missing part in the alpha-decay problem. Escaping the field of the nucleus is by and large a Coulomb scattering problem described quite accurately by formulas written almost a century or more ago. What really matters is the difference between the top of the Coulomb barrier and the alpha-particle energy. Specific details regarding the overall shape of the potential are largely irrelevant for the tunneling process itself. However, a better microscopic picture of nuclear interactions is critically important in order to understand alpha-particle formation. Neither the shell model nor the modern many-body field theories can properly explain this phenomenon.

[@robinswamidasan]

Very interesting.

[@legionreaver]

Where can I learn these kinds of things?

[@thegreatveil5699]

@@legionreaver Depending on the exact meaning of the question, I'm afraid I may not have a good or simple answer. If you're asking about specifics related to nuclear dynamics and particle emission theories, there is of course the specialized literature, but that may be entirely out of reach unless you are knowledgeable in a related field. Textbooks on nuclear physics, particularly the theoretical ones, are typically quite esoteric as well and require a lot of prior knowledge in order to be readable. If however you are more curious about the developments of XXth century physics in general and things like the establishment of quantum mechanics and modern cosmology, there's probably a very large supply of documentary material right here on youtube which can start you off in whatever direction you find interesting. The reason why I like the Physics Explained channel in particular is due to the information being presented in a way which is intelligible to a general audience while also remaining grounded in enough mathematics to not have its meaning distorted and become misleading or downright false. I'm afraid I simply don't know of a channel treating nuclear topics in a similar way specifically, but surely there's something out there if you do a bit of searching.

[@thegreatveil5699]

@dražen g Well, I believe the plates were wrapped in paper and this would have been enough to absorb most alpha particles. However, as I mentioned in my original message, alpha decay is generally accompanied by photon cascades. Particularly in heavy elements like actinides, due to the fact that those systems are generally deformed (the nuclei have an ellipsoidal shape, which is inferred from the structure of their energy spectra). In such systems, a non-negligible amount of the alpha transitions lead into excited states of the daughter nuclei. These states then decay further through the electromagnetic channel by emitting gamma rays. These rays can easily pierce common materials like paper and will interact with the plate. To answer your second question, fluorescence and phosphorescence are indeed slightly different. But for the particular discussion here it doesn't really change anything meaningful. I didn't pick it up in the video, but it's at most a misused term that really has no effect on the development of the material within the presentation.

[@tryagain.k1821]

@dražen g Why do you expect ........ ?

[@thadaeusb6667]

Great summary of a challenging topic! I particularly liked the approximation to the Coulomb potential. Keep up the good work!

[@PhysicsExplainedVideos]

Thanks!

[@RB-fp8hn]

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 :)

[@lucyfrye5365]

Thank you so much for making these. At the risk of sounding unpleasant, there is so little content for people that actually paid attention in high school. And don't get me started on the trend where publishers don't want equations in their pop-science books.

[@ddognine]

Excellent video. I studied Schrodinger's Equation and quantum tunneling in a Physical Chemistry lecture. As good as the lecturer was, I do not recall him demonstrating how to calculate the half-life of a decaying atom with such precision. And the fact that the answer was so close after the the application of numerous simplifications, assumptions, and empirical relationships along the way is astounding which just proves how robust the models are. Gamow and Condon must've had heart attacks after being so far off then so close. Even though I am not a physicist, I have embarked on many mathematical journeys similar to this one in the hope that once I arrive the destination is NY, not LA; I would've certainly given up if I was off by 14 orders of magnitude.

[@petereldergill2942]

I can't believe how many times I've used the phrases ""furthermore" and "ghastly expression" while teaching my classes now. Thanks for the incredibly amazing and in depth, rewatchable videos.

[@michaeld5888]

You have to wonder if there was no internal heating and vulcanism there would be no atmosphere as the sun would have stripped it away by now. It is difficult not to believe that this is as much a problem for Mars as its low gravity. These explanations of the quantum principles are brilliant as even with no deep understanding give an excellent insight in to the subject. I really wish we had this sort of stuff when I was young as we went straight in to the Schrodinger wave equation at Polytechnic, in the days of log tables and slide rules, during the first year of a Chemistry degree and there was a panic amongst the tutors as so few of us had the maths for it. Many thanks for showing us this so succinctly and such a valuable resource for the younger generations.

[@arimunic]

If the core cooled sufficiently then the dynamo action that drives the magnetosphere would shut down. So I think it's reasonable to assume the atmosphere would be stripped a-la mars.

[@pustelnikniqczemnosci856]

I do love your work. Listening to your videos is like having a cup of the best physics tea with delicious mathematical biscuits and just enjoying being overwhelemd with true scientific delight. I am craving for the videos of yours yet to come.

[@PhysicsExplainedVideos]

Glad you like them!

[@bparkinson5397]

Really well explained. I passed A Level maths (C) in 1971 and found maths really difficult. If only I had access to these videos I might have become a particle physicist. Well done and thank you!

[@PhysicsExplainedVideos]

Glad it was helpful!

[@michaelkinney9782]

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!

[@floorpizza8074]

If only I had a physics teacher like you 40 years ago, my life would have turned out a lot different.

[@kanishk9490]

its never too late

[@lucid_]

Remarkable work from one of the most underrated physics channels on youtube 👏👏

[@PhysicsExplainedVideos]

Thank you! Very kind of you to say

[@mrgadget1485]

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.

[@PhysicsExplainedVideos]

Thanks for the feedback, yes, I think that would have helped!

[@hershyfishman2929]

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.

[@qwqwtry7027]

thank you, very helpful

[@MdmanProductions]

Explaining quantum mechanics is truly a gift you have. I look forward to every video you post. Watching your subscriber count grow daily gives me a warm fuzzy feeling for you. Keep up the content

[@PhysicsExplainedVideos]

Thanks, very kind of you to say!

[@glennfellin2953]

Schrodinger brilliantly developed his equations to precisely describe how quantum objects behave. It is nice to see you use the equations to describe how 'alpha' particles can tunnel based on descriptive probabilities inherent in the equations, once again proving these equations are still working well after nearly 100 years. This exercise is circular. The question remains: Why do particles occasionally 'tunnel' through other matter? What is the mechanism? Why do microscopic particles behave like this? 'Why' do they tunnel. Instead of 'can we find a mathematical model that matches behavior?' This is the question we need to answer in the 21st century.

[@peterwan9076]

Your question can be rephrased as asking why quantum objects behave probabilistically? That is the question Einstein asked almost 100 years ago. Bohr answered him (I paraphrase) that is just the way nature is at the microscopic level. That is what Heisenberg uncertainty principle is saying. Things never standstill.

[@MAB68195]

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.

[@PhysicsExplainedVideos]

You're very welcome!

[@haneen3731]

Finally a channel that explains things in detail while still being highly entertaining! Well done and beautiful animation.

[@mdinesh8815]

one of the only channel to actually explain physics concepts with mathematics👍 loved it bro

[@neil1629]

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!

[@abhinandanmalhotra8519]

This guy is just awesome! I would highly appreciate if he creates a full undergraduate Physics Course in the near future !

[@FlockOfHawks]

Well over forty years ago i was sweating seriously on these things , hopelessly lost in horrible differential equations , before i finally grasped the underlying maths and the tremendous power of approximation & simplification I wish i'd had a Teacher like you back then 🙏 ed : come to think of it , there's a remarkable similarity between the tunneling of these particles to the outside world and the tunneling of relevant videos through the barrier of [ YT's algorithms and its 99.9% crap suggestions ] towards the viewer - i'm _so_ glad Schrödinger calculus applies here too , or else i'd never found your magnificent Channel ☺

[@jasonsutton4415]

It is so unusual for a particle physicist to show the maths behind the theory because a lot have the thought that to do so will switch the general public or layman off. But by “doing the maths for us” visually rather than in the background you help to unravel the mystery without losing the audience. The result is more people understand quantum theory than just accept it.

[@PhysicsExplainedVideos]

Thanks for the kind words and feedback, much appreciated

[@roblouw1344]

PE is simply the best physics channel on KZbin!

[@craigfowler7098]

Fascinating stuff. How theoretical models and experimental results agree so closely gives me chills and proves that maths is a powerful tool in exploring the true nature of the universe.

[@PhysicsExplainedVideos]

I get the same feeling!

[@a0756536]

Wow! I felt that I have just seen the best video that youtube has to offer! Wow again!!

[@joaoandrade4402]

That was one of the best videos I've ever seen. It's fantastic. Congratulations on the scientific rigor👏

[@PhysicsExplainedVideos]

Glad you enjoyed it!

[@riadhalrabeh3783]

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.

[@theshowman8478]

What a superb video ! Really well explained and the use of colour for the equations really helps. Terrific. Love this channel.

[@PhysicsExplainedVideos]

Thanks!

[@rajeev_kumawat.]

Congrats on 200k man

[@off7hewall]

This is like an abridged university lecture. Wonderful videos.

[@PhysicsExplainedVideos]

Glad you are enjoying them!

[@kalimeet___1524]

Thank you for not trying to dumb this down and stuck to hard physics 👏

[@Alarich_Vonbergen]

I love this channel. It's refreshing what I learned & it's increasing my knowledge. Thank you for this.

[@juanluisclaure6485]

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

[@PhysicsExplainedVideos]

Happy to help!

[@kanaktiwari2906]

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 ❤🥰

[@PhysicsExplainedVideos]

Thank you so much 😀

[@el-zi4jg]

Really insightful video!!

[@Shaunss]

I just just taken a Modern Physics course and did my final project over quauntum tunneling on a semi-infinite well, but if I had seen this video earlier I wish I had done it over your system with the Polonium atom. Regardless of which, thank you for making this video, your channel has been very entertaining and informative for me!

[@PhysicsExplainedVideos]

Glad it has been helpful!

[@Strothy2]

This channel is prob the best recommendation in the last few months.... great content!

[@PhysicsExplainedVideos]

Glad you enjoy it!

[@ahuddleofpenguins4842]

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.

[@MikeyLikesIt04]

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!

[@edwardarruda7215]

Another excellent video

[@PhysicsExplainedVideos]

Cheers, much appreciated

[@edcoad4930]

@@PhysicsExplainedVideos my comments got truncated. In addition of the one-liner, I applauded you for the brevity of your transmission coefficient derivation (Prof Dave's was good but a little rushed) and I also made a shout out for the tunnel diode. Possibly the funkiest component with its region of negative resistance.

[@stephenlyall7759]

The history of scientific thinking is so important. These early pioneers were at an advantage of a clean uninhabited field. They were at the cliff edge with no tools to assist them but their own immense imaginations.

[@JohnOverstreet]

This is the best explanation for tunneling I've seen! Thank you so much!!

[@PhysicsExplainedVideos]

Glad it was helpful!

[@rudypieplenbosch6752]

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.

[@paulg444]

just fantastic... I would love to hear the author share his insights into the continuity of the derivative of the wave equation and exactly what that constraint is saying about momentum. Is this constraint related to conservation of momentum or energy ?

[@pierluigimartini]

I'm also wondering why the constraint on the continuity of the derivative is necessary. The potential changes in a discontinuous manner, so why wouldn't the derivative? Perhaps the argument is that the potential can affect the acceleration (2nd derivative) discontinuously, but then the first derivative is still continuous?

[@samknott5419]

@@pierluigimartini Take as an example the time-independent Schrodinger Equation. You have to balance the 2nd space derivative of Psi with V*Psi. A discontinuity even in just Psi's derivative would require an infinite potential to balance the equation at that point (and is in fact what happens with an infinite potential well). The general rule is the wavefunction has to be '2 orders more well-behaved' than the potential.

[@cherias.4069]

Excellent! Your mind is 👌✌

[@lepeejon2955]

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

[@Elliott_101]

Thank you very much, your channel is a treasure. i'm really thankful please keep it up!

[@PhysicsExplainedVideos]

Glad you enjoy it!

[@farzanroshdieh698]

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.

[@arturoeugster2377]

This a phantastic presentation, actually very effective teaching, thank you!

[@rocky171986]

Great job! Look forward when you decide to tackle the topic of Bell's Theorem.

[@PhysicsExplainedVideos]

Great suggestion!

[@gzizou_seif]

one of the best content available for free

[@PhysicsExplainedVideos]

Thanks!

[@somebodyoncetoldme1704]

Amazing channel. I studied physics and have a bachelor degree, but having chosen a career in a completely different field, I feel like I forgot everything that I learned. These videos serve as an awesome reminder. I hope in the future you could do videos on electromagnetism (like derivation of Maxwell's equations). I know it's not as 'sexy' as quantum physics but in my opinion it's not any less interesting.

[@DarkKitarist]

Your channel is excellent! It actually made me want to go back to learning physics! Simply brilliant!

[@arjunsinha4015]

Outstanding Lecture

[@PhysicsExplainedVideos]

Thanks!

[@Brianmf]

Beautifully explained. Well done.

[@PhysicsExplainedVideos]

Many thanks!

[@koenth2359]

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!??

[@A3Kr0n]

The video starts at 6:25. Love it. Subscribed!

[@chimaobimartins7280]

Never have I seen a video well discrete in description. this is the best physics channel of all times Thank You, @PhysicsExplained

[@LB-js5ij]

Thank you for making this video!

[@sunilsheth826]

MARVELOUS EXPLANATION, CLEAR AND TO THE POINT

[@tlwmdbt]

Lovely message and vey well explained. All the best to you.

[@sufyanahmed1899]

Interesting content! keep it up, these videos are amazing

[@PhysicsExplainedVideos]

Thanks!

[@abdullahh283]

This is a great explanation, well done!

[@PhysicsExplainedVideos]

Thanks!

[@boiiwizzyy255]

One of the best physics theory i have learned in my life.

[@PhysicsExplainedVideos]

Glad you think so!

[@logicalveganlifts9521]

This was fantastic! Thank you for producing such great content.

[@PhysicsExplainedVideos]

Glad you enjoyed it!

[@HuiBuh]

Very good explanation. Excellent job.

[@_MFender]

I feel like I need to watch that like 3 times and treat it like a uni lecture and I and anyone can learn it awesome job

[@NimrodTargaryen]

Great video, thanks much.seldom have seeing such illustrative video

[@PhysicsExplainedVideos]

Glad it was helpful!

[@paulgrimshaw6301]

The bit that strikes me as rather curious is the calculation of the frequency that an alpha particle attempts to breach the potential barrier. What's the justification for the model that a single alpha particle is vibrating across the diameter of the nucleus? Surely the reality is that an alpha particle doesn't actually exist until it is exiting the nucleus. Until then any set of 2 protons and neutrons within the nucleus (or perhaps on the outside of the nucleus) could potentially tunnel out? How does the frequency of this being attempted relate to oscillation of a single particle across the diameter? And what about the potential barrier of the strong force bonds between nucleons needing to be broken to release an alpha particle?

[@jeromemalenfant6622]

I had the same question; does the alpha particle exist within the nucleus beforehand? Put another way: the nuclear wave function consists of a superposition of various nuclear states. One quantum state corresponds to Z protons and (A-Z) neutrons freely bouncing around inside the potential. Another quantum state corresponds to (Z-2) protons and (A-2-Z) neutrons plus an alpha particle, and so one, (two alpha particles, etc). So the question is, what is the relative magnitude of the second state to the first one? The fact that assuming the alpha particle exists inside the nucleus beforehand gives a pretty good answer suggests that the nuclear wave function has a large one-alpha state component. Another point to consider is that an alpha particle formed from 2 protons and 2 neutrons inside the nucleus has a higher kinetic energy (measured from the bottom of the nuclear potential) than the kinetic energy of any of the nucleons it formed from, due to the alpha particle's binding energy of 28 MeV. Since it sits higher up in the nuclear well, and since the tunneling probabilty increases exponentially with energy, the alpha particle has a much greater probability of tunneling than the nucleons it formed from individually had. Which is why proton or neutron tunneling is much rarer than alpha tunneling.

[@discoverrealityclover9620]

That is exceptional! Bravo!

[@debscat2369]

Thanks for these videos much appreciated

[@gmncnr]

Exactly what i was looking for!!

[@jeremyvirin6532]

I would like to tell you that your channel is the best channel that I have ever found on KZbin. 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😅)

[@jeremyvirin6532]

Or a video about the general relativity ?

[@tamirmichael1265]

Excellent video. Thank you for making it 👌

[@PhysicsExplainedVideos]

Glad you liked it!

[@trsshowstopper9518]

Love your amazing work !

[@PhysicsExplainedVideos]

Thank you so much!

[@shivrajanand2002]

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

[@ahmedamamou7221]

Thank you. I really love your content !

[@PhysicsExplainedVideos]

Glad you enjoy it!

[@ankeunruh7364]

You're a good teacher! Very clear words and presentation, and I love your 'very british'!

[@ta4h1r2]

Awesome stuff!

[@deepak180379]

pure gold .. thanks for the service..

[@PhysicsExplainedVideos]

Glad you enjoyed it!

[@eswarivemuri8937]

Excellent explanation with precise information 👌👌

[@PhysicsExplainedVideos]

Glad you liked it

[@NumbToons]

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.

[@jerzypawlowski7999]

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.

[@The.Golden.Door.]

🔥🔥🔥Thank you for this...definitely using this in my research

[@PhysicsExplainedVideos]

Glad you liked it!

[@The.Golden.Door.]

@@PhysicsExplainedVideos Just had a breakthrough!!! with this equation *⭐🧠 Thank you for the insightful inspiration

[@nicudanciu5758]

What a beautiful explanation! And a very ckear style

[@PhysicsExplainedVideos]

Thank you very much!

[@r.i.p.volodya]

Very interesting and it takes me back to my 2nd year at uni - thank you.

[@skypickle29]

Beautiful exposition. But @ 10: 00 you said Coulomb's law was relevant until the separation of the alpha particle and the uranium nucleus was comparable to the radius of the uranium nucleus.(1.56E-15 m) What well chosen words. The 'paradox' that uranium emits lower energy alpha particles than even higher energy alpha particles cannot even get close to the radius is only the result of the assumption that the barrier to entry should be the same as the barrier to exit. But as anyone knows, it is a lot harder to get into a crowded room than to exit it. So tunnelling probability could be calculated with statistical mechanics as the probability of 'no collisions' But even this is a simplification. The neutrons and protons are not randomly distributed in the nucleus like plum pudding. Rather they are confined to orbitals. This leaves wide swaths (relatively speaking) of space where no collisions will occur by an incident alpha particle. Still the 'average' tunnelling probability is calculable.

[@DingbatToast]

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!

[@wasteKa]

Nice job man.

[@minklmank]

I somehow butchered my way through quantum mechanics during my undergrad years. Despite having to promise my professor to never attend any of his exams ever again after finally passing the last one I am surprised how "easy" this still is for me to follow xD

[@andredavis4657]

Brilliant..... As usual

[@PhysicsExplainedVideos]

Thanks!

[@ratzkykim4204]

Please do a video about Loop Quantum Gravity. I'm curious on how will you create a story out of it and excited to see you go through the Background Independence problem part 😁

[@NeilCrouse99]

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.

[@renscience]

You are amazing Sir. Thank you

[@PhysicsExplainedVideos]

You are most welcome

[@renscience]

I have watched all your videos numerous times. In Spock’s words…fascinating…I know these videos are labor intensive but could you do one on type 1 A supernovas and how QM predicts it? …live long and prosper Renato

[@kevincleary627]

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?

[@mohitsinha2732]

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.

[@narfwhals7843]

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.