Fundamentals of Quantum Physics 2: Superposition. Particle in a box 🌚 Lecture for Sleep & Study
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- čas přidán 14. 05. 2024
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Join us for an engaging scientific lecture exploring the fascinating world of quantum mechanics. Delve into the fundamental concepts of separation of variables and the Schrödinger equation, unravel the mysteries of superposition, and explore the behavior of particles in the infinite square well and the 'particle in a box' scenarios. This captivating session will provide insights into the mathematical foundations and physical implications of these concepts, offering a glimpse into the intriguing nature of quantum phenomena. Don't miss this opportunity to expand your knowledge and deepen your understanding of the quantum realm.
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Table of contents:
0:00:00 Separation of variables and the Schrodinger equation
0:32:10 Stationary solutions to the Schrodinger equation
0:51:36 Superposition of stationary states
1:13:12 Potential functions in the Schrodinger equation
1:35:44 Infinite square well (particle in a box)
1:57:14 Infinite square well states, orthogonality and completeness (Fourier series)
2:21:59 Infinite square well example computations and simulation - Věda a technologie
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5:52 funniest part
"Hopefully you're familiar with some of the terms I'm using here." 😂😂😂😂
0:24: 📚 The Schrodinger equation is solved using separation of variables, a technique for solving partial differential equations.
12:59: 🔑 The relationship between F(T) and G(X) in the partial differential equation requires both F(T) and G(X) to be constant.
27:40: 📚 The Schrodinger equation in quantum mechanics is a simple time evolution equation with a more complicated space part.
40:19: 💡 The time independent Schrodinger equation relates the Hamiltonian operator to the spatial part of the wave function multiplied by a separation constant.
52:41: ⚛ The Schrodinger equation is linear, meaning that if two functions solve the equation, their sum also solves the equation.
1:08:13: 📝 The integral of X1 star X2 is zero, while the integrals of X1 star X1 and X2 star X2 are both one.
1:20:07: 📚 The X function describes a particle attached to a spring, with potential energy increasing as the particle moves away from the origin.
1:33:18: 📈 The potential function tells us about the behavior of the wave function in terms of direction, curvature, and speed.
1:46:53: 📚 The system has a discrete set of allowed energies.
2:01:19: ✅ Orthogonality of vectors can be defined as two vectors being at 90 degrees to each other.
2:15:06: ✨ The time independent Schrodinger equation allows us to express any function as a sum of stationary states, providing a complete basis set.
2:28:24: 📚 The given function is split into two parts for better expression, and the integral is evaluated using the initial conditions.
2:42:29: 📊 The plot shows the time dependence of the probability density calculated with the first 20 stationary state wave functions.
Recap by Tammy AI
I've never heard someone speak chinese with such a good American accent. I wish i paid more attention at school, this is most interesting!
I have a request: lectures on high level nuclear physics. You know, for a friend.
yea, can we have a lecture about how to create a nuclear reactor? just because, don't worry about it!
@@sierra121cyan can I copy your notes later?
@@sierra121cyan can i borrow your nuclear reactor
Oh God, you have a friend who wants to know about nuclear physics? How embarrassing
Legit going to use this video to study.
After I sleep to it.
dog i woke up from sleeping and i was 2 hours deep into this and theyre talking about functions
And?
Thanks! Amazing! What’s the textbook title?
"Lectures for Sleep"
PULLS OUT GRIFFITHS
More videos needed plz upload , waiting man come on!!
I need more of these videos!! Amazing!! Thank you so much!
Am I the only one who woke up to this video?
Thank you for this video.
Has anyone ever said you sound like Topher Grace?
Cn u do for mathematics???
I tried listening to audiobooks to fall asleep to but had to rewind in the morning coz I hadn't a clue what happened while I was asleep, maybe listening when awake will be more beneficial?
I left youtube on over night and now I know the secrets to quantum physics
Did you know our moon is the only Moon that doesn't have a name.
Weird
Yeah it’s the moon “The” singular moon that defines all other moons
I was literally thinking about that the other week 🤔
it does. Luna.
@@dmign ...that's the name to refer to the moons in Spanish
@@daliblue_ in italian
Do one with chemestry
Please do some medical studies uploads.
I don't understand what he's talking about I thought it was about the sun rays and moon's
I genuinely love you channel so much!!
Keep doing what you’re doing, I appreciate it a lot
"don't forget to subscribe" as if I'm not about to fall asleep in 5 minutes
I woke up and this was playing help
It's too late. The ads have us entangled now.
Shoutout Carthage! I'm from Racine and I had to Google the logo. lol it felt soooo familiar
quantum leap reference
Did you say “um”? First minute.
Umx?
Audiobook
too many ads couldn't fall asleep
I can understand every single word he is saying, but his sentences make no sense to my monke brain
Classic autoplay material
I have a new theory about human DNA
What about souls? & Spirit? 🎉😮
@@200fpsASHsoul is immortal
I don't understand it and I don't like it!!! 😢
If you don't understand it after this video, then you never will
@@FlaystrayIt must be hard for you to walk amongst the unwashed masses.
@@scott6129 when they have to edit their clapbacks to something they only assumed was denigrating, yes
@@Flaystray Wow! You get everything right the first time too!