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

[@FortheLoveofPhysics]

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[@jash5586]

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[@delta1996]

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[@DeltaH-9]

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[@harshtiwari7395]

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[@user-eb2mn5nr5h]

Best lecture in my life ❤

[@kevconn441]

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.

[@mohsinshah6857]

Excellent topic...

[@sarthakgirdhar2833]

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.

[@FortheLoveofPhysics]

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.

[@sarthakgirdhar2833]

@@FortheLoveofPhysics Hello sir. Yes I am fine. Yes I agree!

[@lepidoptera9337]

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.

[@sarthakgirdhar2833]

@@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.

[@lepidoptera9337]

@@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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[@payalm2538]

sir plz make a video on perturbation theory

[@swapnilbanerjee1796]

Great but plz upload applications of Schrodinger eqn like partuclein a 1D box

[@hakanegne]

how can Schrodinger equation be applied for protons?

[@usmanphysics6192]

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[@SudhanshuSharmanitdelhi]

sir please provide notes of this lecture very important

[@user-pb7km3tz8o]

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[@FortheLoveofPhysics]

February

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[@cesars.semp.3119]

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.

[@lepidoptera9337]

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.

[@cesars.semp.3119]

@@lepidoptera9337 misplaced video. Sorry.

[@lepidoptera9337]

@@cesars.semp.3119 OK, that makes sense. ;-)

[@mohitz_111]

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[@mazharali5348]

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[@BiswajitDas-fj5gp]

Thanks🙏

[@hozeluii1566]

Excelent!!

[@hectorrajclaudius2562]

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.

[@FortheLoveofPhysics]

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 kzbin.info/www/bejne/aoDbdaZvq8-XmaM

[@hectorrajclaudius2562]

@@FortheLoveofPhysics Thank You, Sir.

[@gok_dogan]

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[@lepidoptera9337]

Electrons don't move. They are quanta of energy of a quantum field.

[@zemm9003]

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.

[@rglennon6872]

Isn’t the SE parabolic?

[@englishforfunandcompetitio248]

Dinger.... Like Finger....not like danger.....so Schroedinger's Equation.

[@user-vy5hf4ei1x]

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[@rishisingh3923]

30:39 where is the - sign gone?

[@FortheLoveofPhysics]

-1/i = i

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[@FortheLoveofPhysics]

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[@lowersaxon]

„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.

[@FortheLoveofPhysics]

Noted. Kindly forgive my linguistic deficiencies 🙏

[@emkopspot]

Focus on lecture not on name 😂😂

[@devanshdewan2597]

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[@Arhankhan0786k]

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