SCHRÖDINGER'S EQUATION (Derivation) - Plausibility Argument & Time-Independent SE Derivation
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- เผยแพร่เมื่อ 20 ก.ค. 2024
- What is the Schrodinger Equation? Can we Derive it? What is it's role in Quantum mechanics?
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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
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Sir, however clearer the lecture is, QM is still a fuzzy subject. Your dedication in clearing the smallest piece of information on QM is really praiseworthy. I was captivated by your presentation. Thanks for your effort.
Another spectacular lecture! You are able to achieve in 55 mins what most instructors cannot in an entire semester.
Brilliant ! Great lecture ! What a way to begin the New Year! Love you so much sir… you are India’s Richard Feynman !
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!
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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
I love your content, sir. Happy New Year!
Thanks for the lecture. i need not even attend the class lectures now am with you to the end....🙏🙏🙏
Well, a good start to the new year. Your QM-viewers really had to be patient.
OMG, you`re a genius!!, love your lectures.
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
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.
Thanks so much, you're saving my semester:)
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
The Best And Best explanation ever❤
Excellent topic...
Very good. Thank you soo much!!
Best lecture in my life ❤
Great lecture. Excellent 👌👌👌
Good day That I have waiting a long time
Good teacher 🎉❤
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.
Loved it
Thank you very much sir it helps me a lot.
Hello Sir......
Kkesy hain app ????
I'm from Pakistan and watch your vudeos daily....
Sir kindly Statistical mechanics py aik lecture series kindly
Allah Bless you with a healthy and comfortable life.
Excelent!!
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 sir.....
.
Can you please tell sir that we'll also do .
1. ATOMIC SPECTROSCOPY
2. MOLECULAR SPECTROSCOPY
xcelent class!
Great thanks
Thanks🙏
Happy new year sir
Thank you very very much sir
Great but plz upload applications of Schrodinger eqn like partuclein a 1D box
Experience Emversity's supportive learning environment firsthand.
sir please videos ki frequency inc. kardo
sir plz make a video on perturbation theory
sir please provide notes of this lecture very important
how can Schrodinger equation be applied for protons?
Sir , when are you going to launch the batch for IIT-JAM/ CUET-PG 2025
February
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Isn’t the SE parabolic?
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.
Hi Sarthak, nice to hear from you. Hope you are doing well. Good point. I chose the plausibility argument as it's the simplest argument to point to The Equation (although Schrodinger himself chose a different path). Given the sequence in which I am introducing these ideas, i have to be careful that I keep the lectures simple. It's one of the demerits about being a teacher - I need to hold the student's hand and lead them step by step.
@@FortheLoveofPhysics Hello sir. Yes I am fine. Yes I agree!
You don't need a plausibility argument. We can derive quantum mechanics directly from Kolmogorov's axioms and relativity. The Schroedinger equation then pops out as a non-relativistic limit of Dirac or gauge field theories. Schroedinger didn't know any of this. He simply guessed correctly. In today's world, however, a teacher who makes handwaving arguments like this simply shows that he hasn't read the modern primary literature.
@@lepidoptera9337 For teaching undergraduates entering their sophomore year, talking about gauge field theories is not likely to play well. By this logic you should start with Peskin and Schroeder's QFT right from the start and derive everything in nonrelativistic quantum mechanics by taking the appropriate limits. Why not even derive classical mechanics by setting hbar=0 everywhere? Surely that is going to help you study rolling cylinders on inclined planes.
@@sarthakgirdhar2833 We don't need gauge field theory to explain the basics of quantum mechanics correctly but the problem is that non-relativistic QM is "miraculous" in a number of ways. The tensor-product structure, for instance, is a direct result of relativity. It does not drop out of a non-relativistic derivation. Neither do important details like fully symmetric bosonic and fully anti-symmetric fermionic wave functions. These require (dimension dependent!) representations of the Poincare group. So in effect we can't even derive enough quantum mechanics with handwaving to get to the periodic table of elements. The buck basically stops at hydrogen. To teach QM to undergrads all the way to Schroedinger and no further produces only one thing: another generation of physicists who do not understand 20th century physics at all. These physicists will then teach another generation of students who will also not understand physics. It's a vicious cycle that we have been playing since the 1930s. Enough already.
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Salam sir..... Plz is topic sy on word notes to update krden plz.... We are waiting anxiously.... Love from Pakistan
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30:39 where is the - sign gone?
-1/i = i
If physicists are able to capture the movements of the electron in an attosecond then it should pose a threat to the uncertainity principle to some extend. Should the fundamental premise of the uncertainity principle be modified in a quantifiable way?. Please post an educative video on the significance of the 2023 Nobel Prize winning work in Physics and its impact on the physicist's understanding of the fundamental tenet of quantum mechanics.
It does not pose a threat to the Uncertainty Principle, as even in Attosecond timescales, we can only get an idea about the change in the probability distribution of the electron-wave, and never pin point the exact "particle" nature of the electron. Nobel Laureate Anne L'Huillier herself mentioned during press release, that their work doesnot impact the HUP. I made a video on Attosecond Physics on my second channel th-cam.com/video/4OxDs9vjdcA/w-d-xo.html
@@FortheLoveofPhysics Thank You, Sir.
To understand HUP
I recommend you to understand deeply how fourier transform come to life .
If you succeed to understand what's the intuitive behind the fourier transform. Then you come across the wave behavior of the particle and try to define its mathematical formula wave-particle model . 💡 Then you find yourself in the middle of the Fourier transform reality. Once you come here 😊 you have to choose red or blue pill.
If you choose a specific k( which is wavenumber) means a you can't define exactly the momentum of the particle. It's weird like the particle itself.
Electrons don't move. They are quanta of energy of a quantum field.
The problem of the uncertainty principle is that it is formulated in a non-invariant way. So it is wrong, but the formulation that is commonly used, not the idea itself. The uncertainty principle tells us that some pairs of quantities are not properly defined, only the product of both (in some sense) matters, it is a physical limitation and not an experimental one.
In words, without formulae: put yourself in the system of reference where the electron is at rest AFTER the absorption. The energy is only the rest energy. Now, from this system, BEFORE the absorption there is a photon, with positive energy, and surely some kinetical energy of the electron, also positive (or zero, but no negative).. Energy is not conserved. As you see, with no formulae, only words, and knowing that those energies are positive. Choose your system of reference well and you will save a lot of calculations.
The Schroedinger equations says absolutely nothing about either electrons or photons. If you want to get to that level you have to quantize electromagnetism and construct a gauge field theory.
@@lepidoptera9337 misplaced video. Sorry.
@@cesars.semp.3119 OK, that makes sense. ;-)
Dinger.... Like Finger....not like danger.....so Schroedinger's Equation.
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„Schrödinger‘s (resp. Schroedinger’s*) equation“ or „the Schrödinger equation.“ But never „the Schrödinger’s equation“. You cannot put a „the“ here. His name is n o t Schrödinger‘s , that would be written Schrödingers. His name is Schrödinger.
So it would be „Das’ equation“ or „the Das equation“ but not „the Das’ equation“. Thats incorrect. Just said, sorry.
* For those who dont have ö on their keyboard, doesnt exist in English, but is common in German and e.g. Turkish, Schroedinger was Austrian and in Austria the official language is German.
Noted. Kindly forgive my linguistic deficiencies 🙏
Focus on lecture not on name 😂😂
theeke bhai tu khush reh