Fundamentals of Quantum Physics 2: Superposition. Particle in a box 🌚 Lecture for Sleep & Study

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

[chrispysaid]

5:52 funniest part

"Hopefully you're familiar with some of the terms I'm using here." 😂😂😂😂

[aanchaallllllll]

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

[AvalanchePerformance]

I have a request: lectures on high level nuclear physics. You know, for a friend.

[Raeff]

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!

[coolfiredude]

went to sleep watching ways the world has almost ended and woke up to being an hour into a quantum physics lecture

[Gregg]

I have a request: a lecture on how to manipulate matter and spacetime. Asking for a friend

[AvalanchePerformance]

Legit going to use this video to study.

After I sleep to it.

[youkilledma]

I left youtube on over night and now I know the secrets to quantum physics

[samiminer]

Am I the only one who woke up to this video?

[blin]

I'm so glad to be taught quantum physics by Eric Foreman

[OscarTheScrapper]

Did you know our moon is the only Moon that doesn't have a name.
Weird

[dylanmcnair]

dog i woke up from sleeping and i was 2 hours deep into this and theyre talking about functions

[jeffknott]

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?

[riyasangar]

I need more of these videos!! Amazing!! Thank you so much!

[NeverEvi]

Thank you for this video.
Has anyone ever said you sound like Topher Grace?

[rakesh]

More videos needed plz upload, waiting man come on!!

[seokkim]

Thanks! Amazing! What’s the textbook title?

[shadowgames]

"Lectures for Sleep"

PULLS OUT GRIFFITHS

[AndreaDesmita]

I genuinely love you channel so much!!
Keep doing what you’re doing, I appreciate it a lot

[petemchardy]

I don't understand what he's talking about I thought it was about the sun rays and moon's