SCHRÖDINGER'S EQUATION (Derivation) - Plausibility Argument & Time-Independent SE Derivation

What is the Schrodinger Equation? Can we Derive it? What is it's role in Quantum mechanics?

𓏬𓏬𓏬𓏬𓏬ELEVATE CLASSES𓏬𓏬𓏬𓏬𓏬

𓏬𓏬𓏬𓏬𓏬LEC NOTES - GDRIVE𓏬𓏬𓏬𓏬𓏬

𓏬𓏬𓏬𓏬𓏬VIDEO DESCRIPTION𓏬𓏬𓏬𓏬𓏬𓏬
The Schrödinger Equation is a fundamental equation in quantum mechanics that describes how the quantum state of a physical system changes over time. Ψ(r,t) is the wave function of the system, which provides the probability amplitude for the position and state of a particle at a given time. The equation is key to predicting how quantum systems evolve over time and underpins much of modern physics.
The time-independent Schrödinger Equation is a key concept in quantum mechanics, used for analyzing situations where the energy in the system does not change with time. This form of the equation focuses on stationary states - scenarios where the probability of finding particles in certain positions remains constant over time. It's particularly useful for studying systems with unchanging potential energy, like atoms and molecules in stable conditions.

00:00 Introduction
02:33 Schrödinger Equation
09:28 Plausibility Argument for Schrödinger Equation
37:50 Time-Independent Schrödinger Equation Derivation

𓏬𓏬𓏬𓏬𓏬𓏬TELEGRAM𓏬𓏬𓏬𓏬𓏬𓏬

𓏬𓏬𓏬𓏬𓏬SUPPORT CHANNEL𓏬𓏬𓏬𓏬𓏬
Your Financial support provides me an additional incentive to create high quality lecture videos. I am very much thankful for your generosity and kindness

JOIN MEMBERSHIP in Youtube 😇😇😇

[FortheLoveofPhysics]

5% EARLYBIRD Discount Coupon available for the first 50 Students before JAN 21. Cheers!

[r.murphy]

Another spectacular lecture! You are able to achieve in 55 mins what most instructors cannot in an entire semester.

[Tom-spgy]

Brilliant ! Great lecture ! What a way to begin the New Year! Love you so much sir… you are India’s Richard Feynman !

[zahidwali]

Your lectures are a captivating journey through the landscape of knowledge. Your passion illuminates each topic, making even the most complex subjects feel approachable. Thank you for making learning such a delightful experience!
❤❤

[jash]

Probably my first and only comment on any video. This video shows one of the most complex and difficult equation in such a manner that no other teacher has been able to show me till now. Really great video sir Thank you so much

[delta]

OMG, you`re a genius!!, love your lectures.

[KibalatsiEmmanuel-tybq]

Thanks for the lecture. i need not even attend the class lectures now am with you to the end....🙏🙏🙏

[DeltaH-]

I love your content, sir. Happy New Year!

[ShivamTiwary-kq]

i am shivam from iit dh. sir its very useful to me and my friends thankss sir

[pete]

Thanks so much, you're saving my semester:)

[kentykatele]

Thank you for the content. I have been studying physics recently as if am at the University. 😅
Please keep it up and make sure we cover all that which is supposed to be covered in quantum without skipping anything

[jacobvandijk]

Well, a good start to the new year. Your QM-viewers really had to be patient.

[anishghatak]

Thanks Sir For Give Us This Type Of Concept... Quantum Mechanics...Books Are Good But when You teaching this type of Lecture ....We Are able To Understand the actual Meaning Of This lines ..Thanks Sir ... For this Kind of lecture ...we Need More ..about Degeneracy, Parity and Liniar Harmonic ossilator Sol ...A lot of things We have To learn From You....Thaku Sir

[niharagrawal]

very well explained super interesting way

[harshtiwari]

Another mind blowing derivation sir I love the way you teach the way you explain things your videos are helping me soo much thankyou soo much
.
Can you please tell sir that we'll also do .
1. ATOMIC SPECTROSCOPY
2. MOLECULAR SPECTROSCOPY

[anirbande]

Sir, Thank you for your constant effort. Could you please make problem solving videos or suggest or attatch problem list with the answer key on the corresponding topics? It is a big request to you. Your video lectures are outstanding but with some problems, I think it will be more helpful to the students like me.

[kevconn]

Hi Proff, Happy New Year and thanks for all your fantastic vids. Looking forward to learning loads more in 2024 on your channel.
Can I ask about a small point someone mentioned to me not so long ago regarding the wave equation.
The WE has a second derivative on both sides. Whereas the SE has a 1st derivative on the left and a 2nd on the right.
It is, in fact, similar to the Heat Equation. Which makes a bit of sense considering the HE is about dispersion over time and that is what solutions of the SE looks like.

[sarthakgirdhar]

Hello sir. Your student Sarthak here.

Even though the plausibility argument does make sense, given that plane waves form a basis for all square integrable functions, I think one important point to emphasize here is the induction of time translation by the Hamiltonian.


In classical mechanics, the Hamiltonian translates the system in time using Poisson brackets. For Schroedinger, time translation using the Hamiltonian was one of the key factors in writing down his equation. Given the fact that we need the time evolution operator to be unitary, since the Hamiltonian is hermitian, the imaginary number i has to automatically enter the formalism.

As you most likely know already, things don't stop here. In further frameworks such as quantum field theory, this is one of the key starting points for writing down the equations of motion, such as the Klein-Gordon or the Dirac equations.

[pipinstallpycaret]

Thank you very much sir it helps me a lot.

[AbdallaDaaMadowe-knjq]

Good day That I have waiting a long time
Good teacher 🎉❤