What is Quantum Tunnelling? 

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

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.

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!

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!

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.

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

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.

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.

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!

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 :)

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

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

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.

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

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.

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!

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

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.

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.

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

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!

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

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.

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.

This is one of the best and most instructive QM exercises, and is a great refresher, or instruction, in the actual mathematics. Do the math!

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.

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

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

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

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

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.

PE is simply the best physics channel on RU-vid!

Great worked-out example. It emphasises why textbooks show a square well potentials is and how you use it in integral form.

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 ☺

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

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.

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.

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

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

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

Congrats on 200k man

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!

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

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.

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

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.

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

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

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.

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

MARVELOUS EXPLANATION, CLEAR AND TO THE POINT

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.

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

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

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

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.

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 ❤🥰

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

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!

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

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

This is a great explanation, well done!

Thank you for making this video!

Really insightful video!!

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

Interesting content! keep it up, these videos are amazing

This is like an abridged university lecture. Wonderful videos.

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

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

Very good explanation. Excellent job.

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

Beautifully explained. Well done.

one of the best content available for free

Thanks for these videos much appreciated

Another excellent video

Exactly what i was looking for!!

That is exceptional! Bravo!

Awesome stuff!

Outstanding Lecture

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

Excellent video. Thank you for making it 👌

Thank you. I really love your content !

pure gold .. thanks for the service..

Love your amazing work !

What a beautiful explanation! And a very ckear style

Nice job man.

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 😁

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?

You are making very good and understandable videos hope you soon join the league of other science educators

Excellent explanation with precise information 👌👌

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!

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!??

i just love this channel ♥♥♥♥♥♥♥

Please sir upload all the videos of quantum physics for Bsc students.Your videos are exceptional.

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 ?

Brilliant..... As usual

Brilliant!

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

This is beautiful

I just love how the solution is simply to allow the partition to be made finer and finer, calculus style.