How Schrodinger Came Up With His Famous Equation (But EASIER)
The Schrodinger Equation is one of the most important equations (if not THE most important equation) in the theory of quantum physics. But where does it come from? How did Schrodinger derive it?
Although it's a quantum form of the law of conservation of energy, its derivation isn't discussed anywhere near as much as it should in my opinion. I've even heard some people say that the equation CAN'T be derived, only verified experimentally.
Luckily, I came across a wonderful paper that outlines a very intuitive derivation. You can find the paper here: arxiv.org/pdf/physics/0610121...
We start with the electromagnetic wave equation - which described electromagnetic waves (as you may have guessed from its name). One of the solutions of this equation is a sinusoidal wave showing the electric field oscillating back and forth between some field value E_0 and its negative, in both space and time.
However this solution is only a solution if a required relationship, or condition, is met. This condition can be boiled down to the idea that any photon corresponding to our wave must have an energy equal to its momentum multiplied by its speed. Luckily, this equation literally defines what a photon is - it's an object whose energy is related to its momentum in that exact way.
Now this relationship (or condition) is actually part of a bigger picture - mass-energy equivalence. For any generic object, we can relate the energy of the object to its momentum and mass through this equivalence relation. For photons, m = 0 so it reduces down to E = pc. However for objects with mass, we get Einstein's famous E = mc^2 equation.
So what if we now go backwards, but starting with the FULL equivalence relation as the condition rather than the reduced one for photons? This way the wave equation we'll end up with SHOULD describe not just photons, but objects with mass (and possibly momentum too). That's exactly what the Schrodinger equation needs to do.
However, when we go backwards like this, the wave equation we end up with is actually the Klein-Gordon equation. This is a relativistic equation, whereas the Schrodinger isn't. So we do need to complete one more step, which is to reduce the Klein-Gordon equation into non-relativistic scenarios. To do this, we see what the equation will look like at low speeds. This is because relativistic effects show up at high speeds, and so if we set the object's speed v to be much less than c, we reduce the Klein-Gordon equation down to the Schrodinger equation!
This derivation is intuitive for those who know the mathematics because we can follow the math through, but it's also intuitive for those who don't know the math because the logical steps can be easily followed.
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Timestamps:
0:00 - The Schrodinger Equation
1:25 - The Electromagnetic Wave Equation and Its Solutions
5:31 - Mass Energy Equivalence - Let's Go Backwards!
7:05 - The Klein-Gordon Equation and Relativity
8:23 - Finally, The Schrodinger Equation (Again)
Videos in Cards:
1:52 - Wave Equation: • The Wave Equation for ...
7:39 - Klein-Gordon and Dirac Equations: • The Man Who Saved Quan...
Пікірлер: 115
Please make a separate video about how Schrodinger came up with the idea of his equation
Yes, show us the original derivation. Thanks.
@rahularyaphysicist
7 ай бұрын
Yeah!!
Yes I wanna see the Schrodinger's process
@shubhkarmansingh4385
7 ай бұрын
Mee too!
@billvvoods
7 ай бұрын
Me three.
@ganeshnachhiringrai744
7 ай бұрын
Me 4
@bsmith6102
7 ай бұрын
and me
@kushagr7132
7 ай бұрын
Me 2
Yes, it would be incredible to see how Schrödinguer derived it. It doesn't matter if the video is 1 hour long👀
Yes! I want to see Schrödinger's way of approaching his equation.
You missed out the potential term in the explanation. Schrodinger also "derived" a hyperbolic version of the equation but dropped it as it didn't predict good results of something which is why he dropped it. I'd be interested in seeing a video on that.
Brilliant content. Thank you for sharing your knowledge with us 🙌
Another great video from you that has made it to the top of my favourites list. Yes please do the other derivation too.
Beautiful derivation. ❤thank you very much.
Would be fantastic to see a video with Schrödingers specific derivation. Amazing content as always!
Thanks for this simpler intro. And Yes Yes Yes to Schrödinger's one Pleaaaaase :) Simply drooling over your own usual incredibly talented coverage of complex matters into layman terms.
This is really good. Spent months pondering many derivations of SE. This looks the best. Will read that paper with interest.
The Algorithm suggested this video to me and it took me ~2 minutes of watching to hit the subscribe button. Great stuff. I'd also like to see how the original derivation was done (and if you wanted to make a particularly long video it would be neat to hear about Feynman's derivation of it thru the path integral)
I'm very impressed with this video. Simple logical steps that get us to Klein-Gordon. Details worked out by the student.
Of course, we'd love to see the separate video. This may just help make the other graspable, but even so... :P
Fantastic videos!
Please also make a video about Schrödinger's derivation Also I love your videos, don't stop making them
Love these videos! 🎉😊
I would definitely love to see Schrodinger's derivation
YES!!! Let's see the hard stuff.😊
Yes, please, show us the original paper of Schrodinger.
This is really interesting. I wish the textbooks would cover this.
Please make a separate video how Schrodinger derived his equation
Yaa make a vedio on schrodinger's equation 👍
the background music is PEAK
Yes, original derivation please.
yo parth! can you make a video on the equation in 2/3 dimensions
Oooo absolutely amazing ❤ I understood it completely....
Yes. Make a video on the original derivation
make video on complete mathematical fornulation of schrodinger equations
Yess for the original method used by Erwin Schrodinger
If light is just oscillating electric and magnetic fields, then are there analogous fields causing the wave nature of massive particles?
Would love to see Schrödinger’s derivation!
Yes we all wanna see how schrodinger came up with it. By the way u have good music taste 🔥
5:30 Another reason for not taking the square root is that momentum is actually a vector, so if you want to take the square root, you have to write the length of the vector p instead of only p. When using the squared form, it's enough to simply write the square of the vector p, no absolute value needed.
How come you get plank constant on both sides of the equation? Could we not simplify removing one h on both sides? Actually I’m used to see momentum squared where it says h squared.
So, based on the presented derivation, what is the meaning of "wave function of a particle" ? Does it mean the particle is inducing some sort of EM field when it is in motion? What if it is a neutral particle? If photon has zero mass, where does it momentum come from? Why is the speed of the particle is less the speed of light inside an atom? Can we calculate the speed?
I've no clue about any of this. I'd never heard of such equation. So thanks for telling me that it is a famous equation.
its nice to derrive through trajetories
Do thisr equation work for relativistic particles? I would suppose not at least with this derivation.
@bjornfeuerbacher5514
5 ай бұрын
Err, did you watch the video? He addressed exactly that question approximately between 7:00 and 8:00.
why is the solution an exponential function and the graph which you made a sine function?
Of course, please make that video
Isnt it from the hamiltonian? P^2/2m + v(x), where P is the momentum operator which can be a gradient for a multivariable function. Historically Heisenberg was the first person to develop the mathematical frame work of quantum mechanics at the time it was called matrix mechanics (BreKet notation was further developed by Paul Dirac which is lives in a hilbert space) , and so he found the momentum operator. Then Schrodinger took the the discreat version of the hilbert space and applied it to all space, creating the schrodinger picture of quantum mechanics. (correct me if I'm wrong please)
@summerQuanta
7 ай бұрын
Schrodinger and Heisenberg initially thought they work on different theories and were not too friendly to each other. Schrodinger was looking for a matter wave equation based on de Broglie's ideas. Such an equation had to satisfy constraints on its dispersion relation which were different from the usual electromagnetic wave equation. On the other hand, Heisenberg's realization was that we should build a theory based on observable quantities and that the order of operations matter. Schrodinger's equation in its initial form is a simplified non relativisic classical field theory, the equivalent to classical electromagnetism for matter. However it can be generalized to fit within the Heisenberg context. In particular, it turns out that the initial Schrodinger equation was just a representation of unitary dynamics in the position basis. But operators such as momentum and position have an invariant meaning independent of the representation chosen. The Heisenberg framework which was really developed over many years by many contributors is quite general. Although any partial differential equation with boundary conditions displays 'quantization' properties for its solutions, this is not what modern quantization procedures are about. Matter is sometimes said to be quantized a 'second time'. In the Heisenberg picture the description of quantization processes and the links with classical physics become obvious if one wants to recover a classical theory in some limits.
@XxAssassinYouXx
7 ай бұрын
@@summerQuanta thank you
I’ll look for the Schrödinger video. This was interesting, actually cool… but I think Klein-Gordon started from the Schrödinger equation. So isn’t that circular?
There is a paper describing a possible "derivation" of Schroedinger (Jaume Masoliver and Ana Ros 2010 Eur. J. Phys. 31 171DOI 10.1088/0143-0807/31/1/016). The idea is that there is no higher theory, based on a given set of axioms, that allows the derivation of this equation. This is pretty much the situation with thebSecond law of Newton which is practically postulated after some reasoning
Bro I am in class 11 My chemistry sir derived the entire equation from scratch and even explained us in just qn hour
Yes, could you please illustrate the derivation of Schrodinger' s from fundamentals . Dldo try illustrating derivation of Einstein 's Equation of General relativity ❤ Thank you so much for creating an interest 💕 ✨️
i remembered first time learning derivation of schrodinger equation was a particle in a box with molecular theory to calculate its energy…..
Very nice. Hopelessly naive question incoming, sorry.. can anyone explain why the localized event we call a 'particle' is considered to pre-exist its measurement? Why a particle is not thought purely to be the interaction of ' measuring' and 'measured' fields?
@Dekoherence-ii8pw
7 ай бұрын
That's not a naive question. It's quite a deep question.
Can u plz shows us an example of how Schrödinger equations is tested?
@bjornfeuerbacher5514
5 ай бұрын
It's tested every day in atomic physics and theoretical chemistry, when spectra and other properties of atoms and molecules are calculated and compared with experimental results.
Does this mean that the electric field of the photon is also its wavefunction?
could you please drive the equation using same method that Scrodinger kimself did.
Why cant particle exhibits wave properties? Take water for example, it is a sea of discrete molecules and it exhibits interference properties. So what is so special about wave particle duality in QM? Isnt it just like water?
Hi bro 👋 , Thank for your as most best explanation to us ❤. As I am science student I understood it clearly. And because of your awesome explanation 😊❤. I request ❤ you bro to make the videos in another language like Hindi. Because it helps lot of us and specially who are not belongs to science field ❤. I hope you make the videos soon in Hindi 😊😊😊😊😊. Thank you for reading my comment 🙏🙏🙏. If you agree ❤❤ for my request give like 👍👍👍 to my comment 👇👇👇.
Original please, also Dirac equation and so on
3:30 the solution of the differential equation is somewhat like k*e^y type. how is this value ever negative??
Yes, I want to see the Schrödinger's way
Is everything an oscillator?
bro's literally Raj Koothrappali from The Big Bang Theory
Please do share about Classical mechanics also example like Lagranges equations also if possible variation of mass with velocity😅😅
I want Schrödinger's derivation
Hello!
🔥🔥🔥🔥
historically, did Shroedinger equation come out of thin air ? I can never find information on how it was build, and to satisfy which experimental result if any
@bjornfeuerbacher5514
5 ай бұрын
It was essentially based on de Broglie's equations, actually similar to the ideas presented in this video, but using more advanced principles like the Hamiltonian formulation of mechanics.
Wh 0:11 y do thecomponent invention of a solar panel to energize a car on the road(in word impulse power
Plz sir make full course on quantum mechanics sir plz with detail understanding of maths as well as physics i am so weak in maths i cant understand quantum mechanics plz sir help me out
Tak!
@ParthGChannel
7 ай бұрын
Thank you very much!
What was Schroedinger trying to drive in the first place?
@joeboxter3635
7 ай бұрын
The equation for the wave assuming it satisfied the uncertainty principal. He knew the answer had to be a wave from observation. He combined the two and arrived at the same last answer.
I just know he did it esoterically, apparently influenced by vedas. I don't know how exactly my research didn't go deep enough, it's sooo buried
Interesting exploration of the dispersion relations, but the derivation seems really ad hoc as it jumps around different areas of physics without bringing any real insight from them. The derivation in Landau & Lifschitz is conceptually very simple and it only refers to classical mechanics. I'm even surprised to find out that western students aren't taught any derivation of this equation at all.
YES DO IT SCHRO'S ONE
O.k. You have my attention.
Ha ha ha ha máster parth, namaste 🙏 🤔Hmm. Schrodinger, my mate... This is like, 😳 This is conservation, bloke, and conservation of energy, pal! 🤣 😳 😟 And a linear transformation 🙄 🧐 If Schrodinger only told them "well 😅 let's find a nice random variable and a neat distribution, then take a lot of samples and then obtaining the probability of every point by 😅 f(phi) ^2" 🤭🤭🤭🤭🤭🤭👋👋👋👋👋👋👋🤓🤓🤓🤓🤓🤓🤓☺️
The complex number valued electromagnetic wave equation solution has an imaginary number inclusive exponent, equal to the square root of non-number negative syntax non-numeral - concatenated with number one numeral 1, resulting in non-numbernumber negativeone representative non-numeralnumeral -1, disqualifying it from quantitative use and Maxwell"s Faradayan electromagnetic induction law equation * suffers from the same problem. * PhysicsFloatHead, "Maxwell's equation explained logically! (Ep 2 : Faradays law powers the world)", KZread.
Parth G
Am I correctly understand that Schrodinger equation cannot be applied to photons because it contains mass in denominator? Also vote for video about original inference of equation
@user-sl6gn1ss8p
7 ай бұрын
I mean, photons are pretty relativistic
But why start with the wave equation if you are trying to describe particles? plus the Schrodinger equation is related to the probability density, not to some measurable field. You need to explain all these things, otherwise the equation still feels fully mysterious.
I want
ye do the video Also here it appears that Klein-Gordon equation was first and Shrodinger made it non-relativistic.
@manipulativer
7 ай бұрын
Also, there is some missconception about a "photon" since it revolves around 1s "action time". Each wave front of a photon is 1 planck, but higher the frequency of light means wave fronts have a shorter duration so it got a greater impulse and or more work done in 1 second. And photons dont travel, they get absorbed and re-emitted continuously, cause only this explains 3 polarizers or bending polarized light
I'm going to have to dislike this one: -You didn't show how Schrodinger came up with it himself, so the title's wrong -You didn't show any of the relevant math, so I just have to take your word for it The overall structure is novel and interesting, but if I want conceptual generalities, that's what the Discovery channel is for. KZread offers the unique opportunity to teach this stuff in-depth.
@user-sl6gn1ss8p
7 ай бұрын
About the first point, that's what the "(but easier)" in the tittle and his explanation mean. For the second point, he does outline the processes and link the actual paper, which goes through the math in 28 steps, so you might like to take a look at that.
@cleon_teunissen
7 ай бұрын
There is another way in which the video fails: in the article that Parth G. links to (Author: David W. Ward) the equation that is arrived at is for a very narrow subset of cases: a free particle. That is: it is for the case of zero potential. So with that version of the equation calculating the hydrogen spectrum is out of scope. I do have to say: in the article it is stated that in his explorations Schrödinger initially set out to come up with a relativistic equation, and that in fact he arrived at the equation that was later named Klein-Gordon equation. Ward writes: "[...] this equation, when applied to the hydrogen atom, did not result in energy levels consistent with Arnold Sommerfeld’s fine structure formula, a refinement of the energy levels according to Bohr" Presumably Schrödinger was simultaneously exploring a non-relativistic approach, and that non-relativistic approach did result in an equation that correctly described the hydrogen spectrum lines. So that is what Schrödinger published. The actual Schrödinger equation does feature a term with potential energy of course. This video (KZread channel: Physics explained), offers a plausibility argument for the Schrödinger equation. (The actual equation, the one with a potential energy term.) kzread.info/dash/bejne/ZIuEo5OFadiwodI.html The plausibility argument is set out to arrive at an equation that satisfies the following constraints: 1. Consistent with the de Broglie-Einstein postulates 2. Must satisfy the work-energy relation: rate of change of kinetic energy must match the rate of change of potential energy 3. The differential equation must be linear: a superposition of solutions must be a solution also. 4. For a constant potential the solution must be a propagating wave (It would be interesting to know who was the first to offer that type of plausibility argument. Another source in which that form of plausibility argument is offered is the book 'University physics' by Young and Freedman. (13th ed. chapter 40, 'Quantum mechanics')) (The discussion in the 'Physics explained' video appears to be modeled on the discussion by Matthias Liepe, Cornell University. Liepe group, Education, Physics 3316, Lecture 10 & Lecture 11)
I like your videos they are very clear. But please let's not promote Schrödinger (the person). His equation can be taught without memeing his face, as he is quite problematic to say the least.
@joeboxter3635
7 ай бұрын
Just pronounce his name as the character on charlie brown.
🤔 I'm starting to watch your explanation. I understand you can't go general, so.. Alright! There is what I was going to nitpick about! The specific solutions of this scenario! 🤝🤓👋 Man, your prerequisites to get this good should be more than what you said and your references to other videos And here is it.. Our SQUARED values 🤓👋 😳 😟 Your still not going to how does fields work in our framework... It's mandatory to get the abstract math, linear algebra framework we use for quantum, brother 🙏😟 😳 There comes the most likely... Mass... EM... Here it comes KLEIN 🤓👋👋 I presume here is the problem, all of the things you are explaining, in college was basically this idea, but you are not manifolding, you are not.. Ok ok, you said "Dirac" 🤓 Not trying to be a bad nerd, professor G. Just I'm a nerd like you but older. I don't believe all these concepts you mentioned here are possible to get for people who not study this branch of science. It's weird from high school physics level of knowledge, and calculus +linear álgebra, and Stats +probability is recommended. And energy is not a Kamehameha but a math relashionship which conserves, symmetry, least action and Noether's theorem 🤓
Those who wants to see Schrodinger’s process 👇
🐱
Whereever you are, the next step is to pronounce the name "Schrödinger" especially the ö:-) properly.
Just waste of time, nothing special in this video. Get fooled after watching this. How this kind of sheets get 35k views ???
Drum roll, please.What haven't you told us why energy is first order and momentum is still second order.Isn't that the most important part?
You are not look much clever