Why The Schrodinger Equation Fails at Relativity

Why did Schrodinger go through with a non-relativistic quantum mechanics, when special relativity was published twenty years before the Schrodinger equation? And how do we know the Schrodinger equation is in fact, non-relativistic?
Klein-Gordon Derivation:
• Deriving The Klein Gor...

[@AndrewDotsonvideos]

A correct submission has been made!

[@K24_ej1]

Andrew Dotson How long did it take you to get to this point in your understanding of physics? My question comes from the fact that I am 27, but only recently decided to change directions in life to push towards my true passion of majoring in physics and seeing where it takes me. Anyways, just curious man. Thanks in advance.

[@possiblepilotdeviation5791]

@@K24_ej1 Romans, I can't speak for Andrew, obviously, but I can briefly tell you my experience. I decided to make a career change when I was 28. I was in a dead end job with no prospects, so I decided to start working on a Physics degree at my local University as a part time student (2 classes per semester). Bear in mind that I already had a degree (art related), so I did not need to take my General Education classes again, just the math and science courses. I kind of had to reshape my entire life. I needed to keep a full time job to pay the bills, so I applied for and finally found a full-time clerical position at the school I was attending. I was able to get a tuition discount from the school since I was an employee, use my lunch break for classes, etc. That was about 4 years ago. I'm almost 32 now. I graduate this coming May. I have a bunch of applications out right now to graduate schools to hopefully start my PhD work in the Fall. If you are dedicated, persistent, and perhaps a bit obsessive compulsive than anyone can learn the material. It's the whole "4 years of your life" thing that will stop most people. It's been a major undertaking, but worth every second for me, especially since I can finally see the light at the end of the tunnel. The material he is covering here is, truth be told, not overly complex. It's certainly not beginner material, but it's not the most complicated either. Good luck with whatever you decide.

[@K24_ej1]

Lyle Arnett, Jr Thank you for the reply Lyle. That definitely gives me a boost in confidence since we seem to be (were) living in the same boat. Dead end job. GE our of the way in college etc. I’ll take note of the things you said. I do appreciate it. 🙏🏻 thanks so much.

[@mikasaackermann8736]

Lyle Arnett, Jr What kind of art did you study, and why did it lead you to a dead end job? Asking 5 a friend

[@carlosvargas2907]

@@K24_ej1 You'll do well, man. Go on!

[@jibran8410]

Lvl 1 crook : Schrodinger Lvl 100 Boss : Dirac *THAT'S HOW QUANTUM MECHANICS WORKS*

[@arroyhondo]

Mike Warrecker that’s how mafia works

[@wotchadave]

What does that make Feynman?

[@ffggddss]

C'mon now, Schrödinger still did a very useful thing there! Just as we don't need even Special Relativity to do a lot of physics, we can still do a lot of QM with Schrödinger's Equation. It gives us quantized energy levels for confined particles, hydrogen wave functions, quantum tunneling, etc., etc. Fred

[@jibran8410]

@@ffggddss Yes I understand, it's just a joke going on around here on the internet with lvl 1 crooks and lvl 100 boss.

[@ffggddss]

@@jibran8410 OK, thanks for the warning. I'll be on the lookout for that ;-) Fred

[@marcusrosales3344]

Huh? Did I just get assigned homework?

[@EpicMathTime]

You are going to be an incredible lecturer and physicist.

[@krishnasimha8097]

Hey epic math time

[@dibidus6080]

Why am I watching Wolverine's lost brother talk about quantum mechanics at 1 am? We may never know.

[@sce2aux464]

And after this video, I watched...kzbin.info/www/bejne/a6imnZeNpM13f8k

[@alexp1113]

Do you hype yourself up before saying, “What’s going on smart people”? It’s always on point.

[@AndrewDotsonvideos]

I'm just naturally hype af

[@WesSlEy954]

I’m proud of myself for being able to keep up with all the calculus going on here

[@Shanksdan]

Glad to have stumbled upon your channel. Physics is really all about asking yourself why something is wrong/ right and actually calculating the answer by yourself (and of course, coming up with a hand waving argument before ).

[@hotlinkster123]

The first time a youtube recommendation has actually been good. Subscribed!

[@AndrewDotsonvideos]

Malcolm Hall awesome!

[@masoomladka5646]

@@AndrewDotsonvideos 😭😂😂

[@pwkn86]

Schrodinger did an OPPSIE!

[@jamestheotherone742]

But still hoodwinked a generation of mathematicians, physicists, sundry academics , politicians, and generals and made off like a bandit.

[@woofle4830]

Both the schrodinger equation and relativity work... so what point is anyone trying to prove here?

[@Nebukanezzer]

@@woofle4830 but not together.

[@woofle4830]

Ohok

[@juanjoserodriguezvera2405]

@@Nebukanezzer exactly and with this demostration we define one of the problems scientists want to solve

[@williamky8842]

The only explanation my lecturers give us was SE doesn’t treat spacetime on equal footing, KG and Dirac does Nice to see some more detailed explanations

[@ElSachinoo]

Nice! Another pre-maths observation: The Schrodinger equation (for a free particle) has a fixed mass value, which is also a relativistic red flag. Another decent exercise: Showing the Schrodinger equation is invariant under Galilean transformations - this also lets you see that mass defines a superselection variable in nonrelativistic QM ('Bargmann mass superselection rule').

[@Ricocossa1]

5:06 This is why we often express vectors of the holonomic basis as ∂i , since there is really an equivalence between vectors and directional derivatives as well as how vectors and partial derivatives transform. In good old flat space this is just a curiosity, but this is crucial in Riemannian geometry where you want to define a tangent space without an embedding. The tangent space can be defined as some abstract vector space made out of directional derivative operators.

[@Lakers661Socal]

I swear physics should also count as a second language.🐈🤯

[@ClayonTutorials]

Math is literally a language, and so is logic. Look up formal systems and formal languages for more information. English is a natural language (along with the rest of the spoken languages).

[@nosirrahx]

@@ClayonTutorials I was going to say something similar. Physics is a nation, they speak calculus there.

[@wolflarsen1900]

math, logic, geometrie are per definition languages. All Equations are sentences about quatitative or countable relations of individual elements of a defined universal set and so on. They all have the same structure as normal languages, they have a syntax, a semantics and a truth value and the only thing which can be true is a sentence (ok in normal language its utterances, which include context and sentence, because in normal languages there is also a context principle)

[@narata1541]

@@ClayonTutorials True, but I'd rather order my food in any other language than math. 😊

[@ClayonTutorials]

@@narata1541 But you should always "order" your internet using math: kzbin.info/www/bejne/kGSsgYmNg5JkodU.

[@thebigoeuph]

For my class that I TA'd for, we actually did that as an extra credit assignment...

[@featherinescat]

In anime world, mentioning Schrodinger will make you smart

[@ThimbaDM]

My god this looks and sounds so tough. I going through high school, studying mathematics and physics and I'm about to apply for a university and try to get my masters in medical physics. Feels like I have a long way to go when I compare my high school material to this. Oh well.. I'm not afraid of hard work.

[@CaridorcTergilti]

Do not worry this calculation Is very easy, just standard derivation and substitution. You will understand It fully in a few years

[@DrGamez123]

doing quantum physics at uni RN, hyped to ask this question in class to make everyone roll their eyes, and for the lecturer to get slightly annoyed

[@yenco4]

Grandioso encontrar un canal así y con tanta naturalidad

[@bobbypederson]

I wish I was able to understand this video so I could do the challenge at the end

[@AndrewDotsonvideos]

What there anything specific that was unclear that I can work on?

[@bobbypederson]

@@AndrewDotsonvideos oh no, it's not your bad, just a bit of a lack of understanding on my part.

[@rufusapplebee1428]

@@AndrewDotsonvideos formulations in applications is algorithms. I am not smart enough to follow formulations, always. Takes me long time to get to the applications, then guess the algorithms and then look at the formulations and definitions of the universes and multiverses. The attempted long term goals of the algorithms is to change the definitions.

[@argentinephenomenologist]

I like the initial explanation, and I love the fact that there's so much I'll get the chance to learn in some time to understand the following part. Greetings!

[@materiasacra]

Instead of working out the coordinate transformation, one can glance briefly at the equation itself. It expresses the non-relativistic relation between total, kinetic and potential energy in the operator form required by Quantum Mechanics: E = p^2/2m + V. This is essentially different from the relation in Special Relativity. Done.

[@commaspace2196]

You could've made this way easier by approximating the whole thing to be 3.1

[@brandonmartin9416]

I don’t know what the hell is happening, and I’m not a physics major, but I continue to watch anyways.

[@sahilnaik3079]

Aha I love these videos. Tell me who doesn't want to watch that after waking up. Great video!!!

[@Ohmau33]

I love coming back to these videos and understanding them a little more each time

[@dXoverdteqprogress]

There was a mistake in your proof. You assumed that the wavefunction is a scalar -- it is not. Let's take psy to be a Gaussian which, at it's peak, has the value p. In a primed frame the value at the peak cannot be the same as p because if you Lorentz contract a function that preserves probability, the peak will be larger. Taking this into account does not save the Schrodinger's equation from being non-relativistic, but people should be aware of this argument.

[@danielplacido8746]

But the wave function is scalar. Complex, but scalar.

[@dXoverdteqprogress]

@@danielplacido8746 Nope. It changes under a Lorentz transformation.

[@dXoverdteqprogress]

@MetraMan09 For a constant velocity, gamma is a constant; it only varies with time when you have acceleration.

[@colfrancis9725]

@@dXoverdteqprogress Wish I had seen this comment before I spent time writing my own.

[@flaviusclaudius7510]

I was always confused when I heard that the Schrödinger equation was non-relativistic, when I knew you could just sub in a relativistic Hamiltonian and it just works (being identical to the Dirac equation); I didn't realise that 'the Schrödinger equation' and 'the general Schrödinger equation' were considered distinct, because I'd always only been taught the latter i.e. id/dt=H. I guess this makes sense now.

[@michaeljburt]

Extraordinarily clear explanation of the mathematics of both Lorentz transforms and how to apply it to an equation involving space and time. Absolutely fantastic. So many folks talking about these aspects of physics have never done the math. It is abundantly clear that you have, likely many times over.

[@mokopa]

3:25 It was at this point that i gave the video a like, and settled in for the long haul

[@pushingpositivity518]

I like your videos. You definitely know your stuff. Also i like your shortcut videos an they way you do integrals & differentiating. Thank you.

[@rituparnakundu2022]

Thank you Andrew for showing the rigorous calculation . I like to point out that without going through the long functional derivative part for the 2nd order term you can just square it. (d/dx)^2 = (rhs)^2. That will give the same result and a big time saver.

[@joaopedroaguiarfmatos1473]

i just saw partial derivatives at university,im feeling really smart for understanding ate least 10% of this video

[@rafaelaguilar123]

Water is wet. Change my mind.

[@AndrewDotsonvideos]

you cant spell water without wet + ar because water ar wet

[@rafaelaguilar123]

*Galaxy brain*

[@waveexistence5742]

Water can't be wet. Wetness is a property of something with water on it. If water has water on it there is just more water, not wet water. You inherently need a second object in which to frame the state of wetness. So a bowl with water in it could be described as wet. But a globe of water floating in the vacuum of space is just water.

[@masskiller9206]

@@waveexistence5742 C-C-C-COMBO killed it lol

[@user-ox5ml5ee9v]

Amazing!😂

[@tapferetomate914]

If you say that the Schrödinger equation is i d/dt [e, t> = H [e, t> it totally works for a special relativistic hamiltonian. The familiar wave equation form of the Schrödinger equation is just it's representation in Position Basis with THE non-relativistic Hamiltonian: H=p^2/2m + V(x) In the case of a free relativistic Scalar particle: H =1/2m^2 * (pI * pI + m^2) where pI denotes the I-th element of Momentum, where I=2 or 3 This is so called lightcone quantization Add a potential V(x) and you're good to go. (you then obviously have a non-free Scalar particle)

[@jeshurunluke5573]

Looks like ur daily upload schedule is always on the dot(son)

[@maxwellsequation4887]

Andrew Son cosθ

[@Zaalatrix]

Great video Andrew! One question though: Since v(x,t) = \frac{ \partial x}{ \partial t }, should't you also differentiate the v^2 terms when you Lorentz transform? Cheers, Henrik

[@marioangelov113]

No, he doesn't differentiate them, because v is constant, so that makes the whole γ factor a constant. Because v is the velocity of the moving inertial reference frame S'. If v was a function of t that would mean, that S' is not inertial, because it would have acceleration.

[@emmanuelfchea]

I am proud of myself that I understood almost 96% of what was presented. I am a Physics major with minor in Mathematics. I still have more work to do. Kudos for the brilliant explanation.

[@addas1392]

Me too...🎉. I am really proud of myself. I did have to rewind on some parts. But I got it. Thank you Andrew. One thing I did not realize until now was how we could apply all the mathematical physics stuff into every derivation and understand that these are correlated. I am so inspired.🎉🎉🎉

[@heavennoes]

me to, I'm going 5th grade and I am proud of myself for finally getting what is going on after a lot of work.

[@christianfunintuscany1147]

Hi Andrew! Regarding the Schrodinger work and the process he used to find his equation it may be useful to read his article on Physical Review n.6 Vol.28 December, 1926. In pragraph n.10 he explains why he didn’t include a relativistic analisis.

[@camilosoares9132]

Do one on the black hole electron (simple math)...i stumbled across that by accident and would like a video and the hypothetical it can be. By the way i deduced it biologically (using physical limit and not mathematical limits). From what i understand that wasn't the first time black holes got over looked ;)

[@worldedit8784]

I'm so happy I found this channel!!!

[@Adam-pv4qn]

I'm so dumb I literally don't understand any of this but I'm still here to support.

[@alexbaykov9221]

Schroedinger started with relativistic equation, the calculations following this approach were inconsistent with experimental results of that time, so he did a non-relativistic approximation, which is exactly the Schroedinger equation we know. When the experiments became more precise, the need for relativistic approach became obvious.

[@Sciencationelle]

I've got a real question. Love your vids, bringing some real physics on youtube, that's juste pure kindness and it is quiet satisfying to watch :) But in your video you said multiple time that "Schrödinger's eq. leads to wave equation" I'm not quite sure, this is what De Broglie said "stationary wave" but in fact all the Schrödinger's eq. solution's aren't wave, the solution are just "stationary state" without the proper form of a wave eq. Anyway that's what I've been told. I would to hear you on that one :) !

[@mango_tree6133]

I have a feeling there are three types of people who watch these videos: 1. The people who actually understand 2. The people who don’t fully understand but want to do physics in the future 3. The people who don’t understand and don’t know why they are here

[@Wecoc1]

1:34 You know this is fucked up when even the Unicode missing letter square is a parameter on your equations

[@aram9167]

goddamn it you sound like an awesome teacher to have

[@AndrewDotsonvideos]

tysm

[@danielbachour9987]

Awesome man! I'm new here! Didn't know about your channel! it's amazing! And of course, already subscribed!! Keep the work going!!

[@thelocalsage]

Really liked this video! Would like to see more like this.

[@doodelay]

Watching this I'm so proud of you bro, you understand this shit like it's second nature. And I know that took crazy effort. Will meet you at the top someday

[@exegetor]

subbed. (decided by the 4min mark) Please keep doing this Andrew!

[@LukeBurns]

It's worth noting that not only is the Schrodinger restricted to the non-relativistic domain, but it is also restricted to the description of electrons in a spin eigenstate! The Pauli equation is a non-relativistic approximation of the Dirac equation that reduces to the Schrodinger equation when in an eigenstate of spin.

[@theultimatereductionist7592]

Which equations should we use for large systems of molecules?

[@ghanshamchandel1854]

Newtons. If wayy to big, then Einsteins GR.

[@qizhengli5685]

Very interesting video! Although I think it will be simpler to derive it if considering the relation of ∂²/∂x²=(∂/∂x)² =(γ∂/∂x’-γv∂/c²∂t‘)²

[@qizhengli5685]

which is to regard the partial derivatives as operators.

[@WmTyndale]

I am glad to see that some American youth are not destroying their brains with music and drugs but are doing something constructive, productive and illuminating.

[@brianel-khoury885]

Love the medium level of rigour. I subscribed. Keep it up.

[@katherinebolwellbyme]

I forgot how to do the chain rule, this was a great explanation/refresher. P.s. I never knew that a mu could be written as a little m.

[@katherinebolwellbyme]

Also it's not pronounced d

[@victorhakim1250]

Hey Andrew. Here's my main confusion: it looks like the Schrodinger Equation isn't even invariant under Galilean transformations! In particular, looking at the final equation you wrote, taking the limits as v/c approaches zero and gamma approaches 1, there still remains the rightmost term of the right side of the equation. Any ideas on why this lingering term appears?

[@victorhakim1250]

Ohhh I've figured it out. That "lingering" term actually needs to be there! (tldr: the Schrodinger equation is in fact invariant under Galilean transformations.) In taking the partial with respect to t', we're taking x' to be constant, not x. But in verifying the validity of the transformation, we have to start with the non-transformed Schrodinger equation, which originally uses psi(x,t) not psi(x',t'). In taking the partial of psi(x,t) with respect to t' (keeping x' constant, not x!), there is an extra term v(delPsi/delx) which is exactly what is cancelled out by the "lingering" term.

[@Calilasseia]

Nice and concise. I could think of a few lecturers who would do well to emulate this performance. :)

[@geoffrygifari4179]

hey andrew, new sub here... i think there was a slight missed opportunity, for if you did cancel the gammas and show in the video the limit of v/c -> 0, you might retain the usual schro's eq with x' and t', thus showing that schro's work in the nonrelativistic limit

[@AndrewDotsonvideos]

Right but at first glance you don't recover the schrodinger equation because there's still the extra factor of d/dx'. You'd need to place more focus on the wave function itself to get everything to come out alright under Galilean transform.

[@geoffrygifari4179]

you're right! my bad

[@AndrewDotsonvideos]

Geoffry Gifari no what you said would totally work, it would just be a lot of effort😅

[@ActionPhysics]

On the same line of thought you will see that gallelian transformation doesn't keep SE invariant. But actually it does. While proving such invariance we can't simply take psi going to psi prime.

[@ActionPhysics]

We have to keep a phase factor then this problem gets super duper complicated

[@TheDarktsun]

I'm wondering if we should interpret this as the Schrodinger Hamiltonian is invalid at high energies, or that the energy is observer-frame dependent...Watching your Klein Gordon derivation next, thanks for the great videos.

[@suryavasanth6893]

I love quantum physics after I saw ur lecture.

[@YdarklifeY]

From the view of someone that is also studying physics that was very well explained ^

[@peterwan9076]

Great work. Keep it up. Enjoy your video very much.

[@IkEisawesome7]

"Things are already going painfully wrong, and that's a good thing." Welcome to physics

[@hbarudi]

Completed this entire major in physics, but still not much info is taught about equations being general relativity or special relativity besides the obvious such as Maxwell's equations and the E=mc2 equations. But I think Schrodinger's equation describes only the wave and simply gives a probability for where the particles is but does not tell the speed of the particle, just its energy and mass are involved. There is particle wave duality and Schrodinger equation focuses on the wave part.

[@quTANum]

I think you can directly square the partial x differentiation operator? It'll be easier this way, since we don't need to apply the definiation of it again.

[@AdityaKumar-ij5ok]

1:36 why physicists always love to forcefully shorten their equation by using alien symbols

[@GeneralPet]

Operators are used elsewhere too

[@emmanuelfchea]

It gives you a better understanding of what happening as you solve the physical problems.

[@bilalhussein9730]

With that particular notation it has two nice uses: it tells you in a millisecond that the equation is Lorentz invariant and makes finding the Green's function extremely simple. It's a lot easier to remember the following: 1) No free Lorentz indices means Lorentz invariance 2) box +m^2 -> 1/(w^2-p^2-m^2) in momentum space. This is just a Fourier transform. Why write more down then you have to? General relativity can get tedious enough to work with using index notation/ differential forms. It would be an absolute nightmare without it.

[@noir935]

Do you struggle with Calc I-III,Differential Equations University Level Physics 1&2 Newtons Laws and Electromagnetism? If you are, make sure to >dotsontutoring.simplybook.me/v2/#

[@isaaccastro7853]

Glad to have just stumbled upon this!

[@mislavnorsic6681]

awsome video, try to add some mic to your place so that sound can be captured when you are not faceing the camera.

[@wolframalpha8634]

You made my day !

[@ThomasGutierrez]

Great content as always. However, \hat{H}\Psi=i\hbar\dot{\Psi} the "Schrödinger equation" does still work relativistically and is used in QFT (with the right Hamiltonian) to evolve the state vector in Hilbert space. The KG and Dirac equations aren't "wave equations" but rather best interpreted as "field equations."

[@zhelyo_physics]

Fantastic video!

[@tuskiomisham]

we learned about the 2d wave equation in my semiconductors class. it's a beautiful thing, but it can't explain a lot of stuff

[@vinirn]

I've subscribed to your channel at the first minute of the video.

[@alapandas6398]

I think the we should get psi'(x',t')=psi(x,t)(1-v²/c²)^(¼) to make the probability in the same region to be equal in both frames. Because probability should be invariant. And this psi' satisfies Schroedinger equation in psi does. By the way I got that equation you wrote but d²/dx'dt' terms vanished. I think I did some calculation mistake.

[@philippjohannsen6217]

Great stuff with this homework thing going on. Looking forward to more challenges :))

[@fatematuzzohora5615]

you are a very good teacher you know that?

[@linuxgaminginfullhd60fps10]

Some people say relativity and quantum mechanics are incompatible. I am new to your channel and don't know if you made a video about it. Yet you need relativity in any physical theory to properly describe magnetic field. In quantum mechanics you would need Dirac equation(which is relativistic!) to derive spin. Some people talk about black hole entropy paradox(as one of the reasons why they are not compatible). Wasn't that resolved years ago? Others talk about "quantum teleportation"... which does not transmit information, thus does not violate finite speed of information transmission(aka speed of light).

[@treborheminway1196]

Question:If entanglement is a defining aspect of QM,why would you expect relativistic terms in equations describing it. Isn't that essentially why folks like the whole " The universe is a hologram " idea? Doesn't entanglement mean there is no spacetime at the am level????

[@mattheweverette6911]

I wish I knew some physics :'(

[@lanevotapka4012]

What role would velocity "v" play if your final result? I know that v isn't well defined in QM, and that the Schrodinger equation doesn't use velocity. So how can you combine the v from the Lorentz transform with the Schrodinger equation?

[@beetehotraroy3468]

The 'v' is the velocity of the moving frame of the observer, with respect to the frame of the previous observer who was previously viewing the system and describing it via the Schrodinger equation. Particle velocity is, indeed, ill-defined in QM, but the velocity of the frame is well-defined. If Schrodinger equation were a relativistic equation, it should have been of the same form, as viewed from any non-accelerating frame, which is the first principle of relativity. Now, from the second principle of relativity (speed of light is same as viewed from any non-accelerating frame), we obtain that the correct transformation law between the space-time coordinates is the Lorentz transformation. So, Schrodinger equation should have been invariant under these transformations if it wanted to pass the test of being relativistic. The whole point of the exercise was that it fails to do so. P.S. - I apologise if I am not able to explain it properly. In that I hope someone can do it better than me and to your satisfaction. All the best.

[@lanevotapka4012]

@@beetehotraroy3468 Yes, this answer makes sense. Thank you.

[@subramanyam2699]

Got so many connections in one video.. Tnx :)

[@deeptochatterjee532]

If there was a lorentzian invariant hamiltonian would it work? Like for example H=cP for photons?

[@mathunt1130]

The Schrodinger equation is a parabolic PDE, therefore it has an infinite speed of information propagation. If you want an equation for quantum mechanics that has finite speed of propagation information then your equation HAS to be hyperbolic.

[@largewoollybugger]

Andrew: I need more rigor Whiteboard: But, only (at most) 3 things are defined?

[@acatisfinetoo3018]

I don't understand why the chain rule is used. My understanding is that it's used to solve composite functions, but i only did Calc one so this level of math is a bit beyond me...

[@zokalyx]

Oh no... Your schedule will mess up with mine if you start doing these pbs-like competitions. You literally upload right after I go to sleep (I'm here now because it's saturday).

[@AndrewDotsonvideos]

Hmmm, actually, quantum mechanics forbids this

[@bilalchughtai_]

Shouldn't you consider a multiplicative phase onto the wavefunction? When showing the Schrödinger equation is invariant under guage transformations for an electromagnetic potential we pick up such a factor in the wavefunction!

[@SkanderTALEBHACINE]

Why haven't you supposed that Psi will also (after Lorentz transf) change to Psi (prime)?

[@pipertripp]

Good craic. Enjoyed even if I have only the dimmest understanding of quantum mechanics.

[@ikkebrikke]

Hi Andrew, I was wondering what your opinion is on double majoring in physics and mathematics. I'm in my last year from high school and i'm in doubt whether to just do physics or do a double major. Thanks in Advance! Love your vids

[@jcd-k2s]

Maybe we should stop with the Shroedinger equation? I don't know a single object following the Shroedinger equation. What's the wave function of a photon? Hard to define, but in lots of cases, either the 4-potential Amu, or E+iB can fit. Therefore I wonder why we use a klein gordon equation for photons and not directly a 1st degree time derivative from maxwell's equation as an evolution equation. Like (d is partial) ) d (E+iB) /dt = i rot ( E +iB) (forgetting constants and sources terms) It's really fascinating, QM is supposed to be a phenomenon englobing the whole world, where everything interferes with everything. But in reality we still need specific evolution equations for specific objects. For example Dirac equation for fermions, and Klein Gordon equation for bosons. And second quantization pushes that specificity further.

[@beingphysicist4180]

Thank you sir .

[@okmijnbhunji1316]

but lorentz transform is only for the special relativity right? should we work in functional form for the coordinate transforms, it would be more general i suppose.

[@OBGynKenobi]

Which brings up a question. Where is the line between relativistic and non relativistic. For example up to what limit does Schrodinger equation work? ie, what is the fastest speed an electron can go and Schrodinger still works?

[@AndrewDotsonvideos]

Go Mezant The answer is always “it depends on the error you’re willing to accept”

[@johnjames4194]

I love this channel 😂😂

[@arnoldbirkenhager1290]

Ha! You missed two primes :). Wouldn't have given you another result though, since you only forgot to write the primes and continued calculating as if they were there. Good job! Enjoyed the video and could follow along, but couldn't do it myself. A new Feynman in the making? Hope you aspire to be a teacher. Thanks!