The Time-Independent Schrodinger Equation

Рет қаралды 38,114

4 жыл бұрын

Explaining and deriving the time-independent #SchrodingerEquation using separation of variables to break up the full Schrodinger equation.
Questions/requests? Let me know in the comments!
Video on separation of variables in PDEs: • Solving the 1-D Heat/D...
Prerequisites: The videos before this one in my #QuantumMechanics playlist: • Quantum Mechanics
Lecture Notes: drive.google.com/open?id=12po...
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Twitter: / facultyofkhan
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Пікірлер: 38

@thetheandrein 4 жыл бұрын

I admire you a lot. All the doubts that have passed across my head, and that I never could wrap my head around, you just explain them, and I don't know if you have encountered these problems along your studies and, for that reason, you just emphasize those aspects, but God... I love your videos, maybe you are my way through quantum mechanics. I study chemical engineering, but I have always loved these topics.

@oyugioyugi6018 4 жыл бұрын

4 videos in 1 week🤯🤯 covid works hard. But Khan works harder😤

@jacobvandijk6525 4 жыл бұрын

Why these comparisons with KA? This is a different level.

@FahimusAlimus 3 жыл бұрын

@@jacobvandijk6525 is there any connection?

@jacobvandijk6525 3 жыл бұрын

@@FahimusAlimus Don't think so. The other Khan explains mostly high-school material. This is at an academic level. Different stages on the learning curve.

@FahimusAlimus 3 жыл бұрын

@@jacobvandijk6525 I thought they had some connection

@jacobvandijk6525 3 жыл бұрын

@@FahimusAlimus Perhaps through this man (haha): en.wikipedia.org/wiki/Genghis_Khan

@sunnivagravdahl6816 3 жыл бұрын

Amazing explanation, and exactly what I needed. Thank you so much!!

@averagecornenjoyer6348 2 жыл бұрын

this is all so tidy, I love it

@sairojalin1569 3 жыл бұрын

I am surely in love with ur voice and the way of explanation .

@jacobvandijk6525 4 жыл бұрын

I guess the next step, to the Klein-Gorden-equation or even the Dirac-equation, won't be so big now. But will he (once) do it? Or even a series of videos on QFT??? ;-) I hope so! For those who can't wait (like me), the last reference of this Wikipedia-page is worth reading; understanding it is another thing: en.wikipedia.org/wiki/Dirac_spinor

@jatinbhatia4954 4 жыл бұрын

hi! What software do you use for digital black board???

@sindycross3401 4 жыл бұрын

Thank you for your lesson! I have a question: at around 5:47 , when you prove that both sides are constant, what if x and t change simultaneously? At least V(x) is changing, right?

@FacultyofKhan 4 жыл бұрын

If you agree that 1) when t changes, both sides are constant, 2) when x changes, both sides are constant, then it should follow that 3) when x and t both change, both sides should still be constant. Alternatively, you can differentiate both sides with respect to x and t, you'll get zero. Hope that helps!

@tejassonawane7137 3 жыл бұрын

How did you get the extra tau after substitution at @4:47 in the RHS?

@girishtripathy3354 3 жыл бұрын

Where are the other videos of this series? Mr. Khan

@mastershooter64 2 жыл бұрын

Lol in 8th grade I was reading a pop science book about quantum mechanics and my sister told me "you need really advanced math to study this" i was like "aw :(" now im in the 12th grade and im reading an actual textbook on QM lol and the math is actually not too bad lol

@mathapplication 3 жыл бұрын

You are good!!🙆🏽

@captainhd9741 3 жыл бұрын

I'm confused about something. E^ is the energy operator and E^ operating on tau equals ih`d(tau)/dt but here is the problem. My lecture notes rearranged and divided through by tau to give E=ih`/tau d(tau)/dt but is that even allowed mathematically? I feel like this is such a huge problem. E^=ihd(...)/dt so E^tau gives ihd(tau)/dt and so the 1/(tau) seemed like an addition. This is like calling f=d/dx and then saying fy=dy/dx but then rearranging to get f=dy/dx divided by y (remember f=d/dx not dy/dx divided by y).

@duf2 2 жыл бұрын

what does a boundary condition mean ?

@menot5039 3 жыл бұрын

good job .

@jitendeka5619 3 жыл бұрын

Thank you

@ostensiblyquerulous 4 жыл бұрын

This man is incredible

@rushikeshm1337 2 жыл бұрын

7:40 , what does it mean that A is absorbed by small psi ?

@thewrestlingrebel3108 6 ай бұрын

I think he included that constant with the small psi function.

@SeemaSharma-ot5vh 4 жыл бұрын

Sir why the wave function collapse after measurement and change after every measurement

@JivanPal 4 жыл бұрын

The notion of wave function collapse only arises if you treat a subset of the environment as a quantum system, and the rest as a classical system. The way in which quantum measurement/observation manifests itself within a classical system is as a collapse of the wavefunction. However, if one exclusively uses quantum mechanics to describe the entire environment, then no notion of wavefunction collapse is encountered; instead, it is thought that macroscopic effects manifest through decoherence of the many wavefunctions that the environment consists of. In particular, wavefunction collapse only really poses an issue to human sensibilities in the context of the Copenhagen interpretation. For example, if we consider the Everett ("many worlds") interpretation, there is no notion of collapse; all possible macroscopic/classical observations occur disjointly in their own versions of the universe. There is also the de Broglie-Bohm ("pilot wave") interpretation, wherein the problem of wave collapse explicitly never arises (the wavefunction never collapses) and is instead handled by "hidden variables" - things we cannot currently measure. See here: en.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory See also: • quantum decoherence - kzfaq.info/get/bejne/fdJ_qq2Ir720hac.html • quantum measurement problem - en.wikipedia.org/wiki/Measurement_problem • various interpretations of quantum mechanics - en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics

@christopherwalsh3101 4 жыл бұрын

I dont know whats happening, but it looks cool!

@jacobvandijk6525 4 жыл бұрын

Haha, that's exactly how I felt a year ago. Start asking!

@nicemwaura857 3 жыл бұрын

Great content delivery. I just found you too fast though. Just reduce the pace a little, you are excellent

@allawhussein 3 жыл бұрын

In the name of my class mates and my self, we thank you, we are sorry, we can't donate thought we want, since the banking system in my country collapsed