The Quantum Barrier Potential Part 1: Quantum Tunneling

Now that we've covered the particle in a box, we are familiar with the concept of a quantum problem. Let's move on to our second quantum problem, that of the quantum barrier potential. With this one, we don't have an infinite square well containing a particle, we have a free particle that encounters a barrier of finite potential. This is a good model for an electron that encounters a defect in a wire. How do we know if the electron will be able to traverse this barrier? As it turns out, even if the energy of the electron is less than the barrier potential, it may still be able to be transmitted due to a phenomenon called quantum tunneling. This is pretty weird, but entirely rooted in sound mathematics, so let's go over the math and learn more about this freaky concept!

Script by Hèctor Mas

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[peterpan]

I’ve been waiting for more videos on quantum physics for

[petsan]

Flat earthers be like: I don't see any curvature on that x-axis, you played yourself Dave.

[peterbalogh]

Just a few hundred hours more and I will say: AHAAA! Thanks! :-D

[fougcrm]

14:22 Could someone explain to me, how we come to the conclusion that the A term describes movement to the right and the B term movement to the left?
Especially, since we are operating with time independent solutions.

[astrolonim]

I'm a third-year physics student in college and this is by far the best explanation of QM I've seen. Would love more higher-level physics and math videos from you (Differential Eqns, Schro Eqn in more complex situations (like in an atom), quantum numbers, etc). Thank you so much more producing this stuff, you, Pauls Math Notes, and MIT OpenCourse are the best resources on the internet.

[asylumskp]

Quantam Jesus strikes us again with fax and knowledge

[pablog]

From a struggling physics student, THANK YOU
You have no idea how this material has helped me and my classmates, from the bottom of my cold engineering heart, thank you!

[petloveraw]

its 2am.. i graduated highschool a year ago.. i am not in university.. what am i doing here-

[fwame]

ah, yes, the reason we cant have faster chips

[glennpearson]

This is getting deep! No wonder you have to chop this up into so many parts. Thanks for your patience in plowing through the math for us, Professor Dave.

[removed]

When are you going to do gaming videos

[hkypcwv]

Exactly when I'm thinking and studying QM... thanks for the great work! Keep it up Dave!

[ag_]

So, a particle with Energy (E) < Potential Barrier (V) can penetrate the barrier. Quantum Mechanics is really spooky!

[ianlee]

I can't even begin to put into words how much this series has helped me understand quantum mechanics. Don't stop making such videos! People need you!

[mjzudba]

I'm... Early... For the second time in a row! Yes!
Also, I love you Dave and your videos. Good job, well done, keep going! 😊
Edit: your* videos.
Sorry 🙏😅

[tommysheehan]

I’m taking theoretical mechanics next semester, this series will definitely be rewatched lmao

[siddarthadhanukonda]

It should be -k_above^2 instead of +k_above^2 at 13:25. You already corrected for the sign by changing (V_ 0 - E) to (E - V_0). This gives the complex exponential solution to the ODE.

[chiara.m]

I just got the covid vaccine and I'm very exhausted at 11:30 pm. Not the best time to watch this, but its so interesting to me🤣

[hyeonsseungsseungi]

Could you explain schrödinger equation for hydrogen atom?

[lindaedvardsson]

Ooh.. Your 20 min vids tend to become more like 2 hour every time...🥴.. Never paused the best p**n as much😬🥴...😅🤣..