The Electron Wavenumber k

/ edmundsj
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In this video, I explain the wavenumber k, where it comes from in quantum mechanics, and why it is incredibly useful in solving the Schrodinger equation. In my experience, much of the difficulty in understanding quantum mechanics arises when trying to understand the wavenumber, so I thought it deserved at least one of its own videos.
This is part of my series on semiconductor physics (often called Electronics 1 at university). This is based on the book Semiconductor Physics and Devices by Donald Neamen, as well as the EECS 170A/174 courses taught at UC Irvine.
Hope you found this video helpful, please post in the comments below anything I can do to improve future videos, or suggestions you have for future videos.

[@firmkillernate]

I'm working on my PhD and I need to learn about solid state physics. I've seen a shitload of word salads regarding k, and you just summed it up with "spatial frequency". Thank you!

[@p.b.2903]

I agree. This guy is very astute and he has a true deep understanding of the fundamentals. He is inspiring.

[@kencondon1772]

These videos are the perfect amount of depth for a practical semiconductors review. Thanks for posting!

[@JordanEdmundsEECS]

Thanks for commenting :D

[@wuyizhou]

Why is the explanation so clear!!!! couldnt find much on wavenumber until i came here :DD

[@abdou290]

The second term of the schrodinger equation at 8:11 has a small mistake. It should be 2m(E-U)/hbar square

[@ruicao7054]

yes you are right sir

[@arjunp7765]

Thanks Jordan . This indeed helped me to unravel the mystery of "wave number"

[@priyanksharma4178]

So simple and beautiful!

[@alexanderheller2039]

Brilliantly simplified, thank you very much

[@mayteylg]

This was sooo clear! Thank you very much!

[@jessereynolds9013]

Thanks, great simplified explanation

[@aselim20.]

I watched it and took notes.

[@pitv1315]

Thanks for the video🙂

[@manup263]

Great playlist! When deriving the equation for k as a function of m and E it is probably a bit more straight forward/convenient to use E = p^2 / 2m and substitute p = hbar k from which the equation at 7:37 follows directly.

[@JordanEdmundsEECS]

You are 100% correct and now that I’ve actually taken quantum mechanics from the physics department I understand this now. XD

[@ankur1888]

@@JordanEdmundsEECS LoL

[@xltian4368]

One way that works with me to intuitively understand k is the analogy of the pencel sharpener.

[@MerlinusAmbrosius]

I've found a gem

[@mahmudulhasanrussel2673]

Satisfying feel❤

[@jdavidrhea]

I don’t even understand advanced mathematics, but for some reason I love watching these videos. Is that wrong?

[@placatedlipid3385]

go play Symbolab and Khan Academy one hour a day for the next year and you can come back to this video and completely understand I promise, I started from prealgebra and it's all clicking now-- best of luck if you do choose to do so, you can do it.

[@mechanicclemont4799]

Professor, What program did you use to make this video???

[@xAmiSarahx]

I like it

[@FNS_chn]

thank u)

[@nadarasarbahavan6269]

So how can we relate the Broglie equation with E =hf.. BEcause one is a talking about a spatial wavelength and the other is talking about a time wavelength?

[@JordanEdmundsEECS]

Beautiful question. This will depend on the relation between energy and momentum (called the dispersion relation) of the system. For a free particle (no potential energy) it’s just E=p^2/2m, or the kinetic energy of the particle, and you can solve for k. For systems with a potential energy, it’s more complex, but often boils down to a similar answer.

[@DW-iq8lt]

@@JordanEdmundsEECS I feel like the E at 8:03 is different of the E at 7:32. So at 9:03, the k E doesn't means the relation between "wavenumber and the particle's kinetic energy", but mean "wavenumber and the particle's total energy", right?

[@HUEHUEUHEPony]

Why do we substract the potential energy?

[@fongchienyoong7656]

It has to do with the Lagrangian formulation. sciencemeetsfiction.com/2020/07/04/why-does-the-lagrangian-equal-t-v/

[@jacobvandijk6525]

@ 3:02 With position (x) along the x-axis this is NOT the period, but the wavelength! So this isn't correct too: 3:33.

[@tahseenomar]

I watched this and clapped

[@lionelmartinez6810]

Please, subtitles in Spanish

[@JordanEdmundsEECS]

Know any translators?

[@lionelmartinez6810]

Jordan Edmunds kzbin.info/door/URzsoZzNIelGjI_4zOJ2cA he translate some videos of @3blue1brown

[@lionelmartinez6810]

kzbin.info/www/bejne/eYq6Zoeqfq91nc0

[@HUEHUEUHEPony]

@@JordanEdmundsEECS you know you can allow people to translate it for you in youtube, like crowdsourced subtitles, so you barely need to do any work, just activate the option on youtube.