Dealing with Schrodinger's Equation - The Hamiltonian

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Schrodinger's Equation is a beast of a thing. Fortunately, some very smart physicists have figured out ways to deal with it that don't require a full 30 seconds of writing every time you have to use it. This video is about how I like to deal with the schrodinger equation, and I also describe how to arrive at the time-independent equation from the time-dependent one using separation of variables.

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.

[adrianaugarte]

Best video about dealing with the Schrodinger time-dependent equation !! Thank you so much, you're making studying for my finals way easier and refinding the motivation for theoretical chemistry again !! :)

[PetitCorpsSalade]

My physical chem professor (Mr. I-taught-at-the-MIT) doesn't even take the time to reply to students requesting a book reference to study the course material in-depth, and you take the time to reply to YT comments.
You are passionate and your explanations as clear as a material with an infinite band gap!
I have my very last final before (hopefully) graduating from uni and getting my master's in chemistry after 9 years (I have a full-time career). If I do graduate, you'll be partly responsible, and either way thank you so much for your videos!

[jy]

Super clear! Your explanation is so beautiful!

[maryfucci]

So thankful to have found your channel! You have been helping me understand the bigger picture of my solid state physics class and I am able to make a lot of connections with my atomic physics and lasers class. Much appreciated!

[hamsalak]

Magical. First time here in your channel and the only thing I can say is that. Great explanation I am looking forward to browsing your channel

[manishmitadutta]

the moment he called it gross i already loved him!!!😍😍😍

[lebecccomputer]

0:51 I had so much orange juice in my mouth and it almost went everywhere bro lmao

[klimentbabushkovski]

Thanks for the simplification, it sounds great!

[landdevil]

around 9:05, when you made H psi(x) / psi(x) = E, can we simply move the psi(x) to the right side, and get the H psi(x) = E*psi(x), which is the time independent schrodinger's equation?

[probro]

Perhaps I missed it, but I don't think he quite explained why E is the total energy of the particle.

[vineethsasidharan]

hi jordan i have become a fan of you !

[cmdrbobert]

I loved the video, but I'm just lost as why/how you knew to put the -iE/h into an exponential. I wouldn't have made that leap without seeing it, but I don't understand why you can do that.

[msergejev]

We share the spectrum of emotions about non-compact and non-elegant solutions :)

[deepbayes]

Really nice, is there a full playlist on quantum mechanics?

[lanaalabbasi]

Thanks a lot for making this video! It was very helpful. Where can I find the following videos on solving for the time-independent form of the equation?

[Mattpl]

At 7:27, do you mean to say that H IS a function of x? The annotation above says that H is a function of x

[deerghshahi]

please could you explain the importance of Hamiltonian in quantum mechanics?

[Zucchi]

I love how most functions are gross and I can't agree more
They're hecking disgusting