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
The Quantum Story - Jim Baggot
Quantum Physics for Dummies - Steven Holzner
Thirty Years that Shook Physics - Gamow
Inward Bound - Abraham Pais

[farzanroshdieh]

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.

[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.

[jameslockwood]

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

[samw]

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!

[petereldergill]

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.

[stevecraig]

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!

[thegreatveil]

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.

[thadaeusb]

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

[michaelkinney]

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!

[RB-fphn]

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 :)

[hershyfishman]

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.

[lucyfrye]

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.

[bparkinson]

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!

[pustelnikniqczemnosci]

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.

[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.

[floorpizza]

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

[haneen]

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

[lucid_]

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

[a]

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

[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