The True Meaning of Schrödinger's Equation
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Күн бұрынSchrödinger's equation governs the behavior of tiny quantum particles by treating them as wave functions. But is Schrödinger's equation actually a wave equation? Maybe not.
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TIME CODES
00:00 Cold Open
00:24 Viewer Question
01:02 Strings
02:41 Wave Equations
03:42 Where does it come from?
04:43 Schrödinger's Equation
05:29 Language is Complicated
06:28 Arvin Ash Collab
07:36 Heat Equations
08:18 Probability Flow
09:56 Summary
11:02 My Book
11:17 Other Quantum Equations
11:48 Outro
12:00 Featured Comment
#quantummechanics #quantumphysics #schrodingerwaveequation
@ScienceAsylum Жыл бұрын
Don't forget to check out Arvin Ash's video on the ubiquitous harmonic oscillator: kzfaq.info/get/bejne/eMCCqZt_0NWdiIU.html 🤓
@LuisAldamiz Жыл бұрын
So it's not any coincidence that Arvin's video an yours popped up in my notifications almost simultaneously. I knew it: coincidences do not exist! 🤔
@En_theo Жыл бұрын
It's okay to be a little self-promotional for time to time, Nic :)
@PMA65537 Жыл бұрын
If I made videos and mentioned Arvin then just for that part of the video I'd be wearing an Arvin-type hat.
@ArvinAsh Жыл бұрын
Thanks for the collab Nick! It was fun. Your video is not only funny and creative, as usual, but also important!
@ScienceAsylum Жыл бұрын
@@clmasse Fair point. It would have been more accurate to say "seemingly ubiquitous."
@shelley-anneharrisberg7409 Жыл бұрын
This is the first time I have really understood why the wave equation is written as it is! We did the derivation and how to solve it, but I never fully understood it. You are an epic genius at understanding and relaying physical concepts! The same for the heat and fluid equation and explaining the "flow" of probability in the Schrödinger equation. I am so grateful :)
@ScienceAsylum Жыл бұрын
Glad it helped! 🤓
@pwinsider007 Жыл бұрын
@@ScienceAsylum orbital is created by assuming position of particle is uncertain and velocity thus energy of particle is certain but what would an orbital look like if it is created by assuming postion of particle is certain and velocity thus energy of particle(energy of orbital) is uncertain?
@sardamdar Жыл бұрын
Exactly, I always wonder if I'm not listening in classes or the teachers don't teach well.
@ToriKo_ Жыл бұрын
This exactly! First time I’ve been introduced to the idea that there are ‘standard’ heat and wave equation, shown what they look like, and shown how the Schrödinger equation fits into that, instead of just falling from the sky
@Patrik6920 Жыл бұрын
@@pwinsider007 ..orbitals is a costruct of humans ... it makes it easier to work with just... in reality thers no such things as orbitals..but energy stats...the probability that a higer energy electron is further away from the nucleus is bigger...but its a it all over the place... i see iyt as a rather fundamental misconception thats been passed down in time... the real interesting q is 'Why does waves behave as particles when intersecting' and not 'why does particles behave as waves' (there is no particle...its an illusion) thankfully soundwaves behave very simillar and can be used explain it (it make it easier for us sapiens to comprehend it)...let it sink in b4 u answer...
@stevenjones8575 Жыл бұрын
Dang, a flow of probability makes a lot more intuitive sense to me than a wave of probability. Thanks for the awesome video!
@ScienceAsylum Жыл бұрын
Glad I could help 🤓
@DrDeuteron Жыл бұрын
It only makes intuitive sense when you ||psi^2|| it...I don't think intuition covers a flow of complex probability amplitude. That gives me an idea.
@bozo5632 Жыл бұрын
So, what, probability particles are moving?
@DrDeuteron Жыл бұрын
@@bozo5632 no, that's (psi*)grad(psi) -(psi)grad(psi*).
@UteChewb Жыл бұрын
I remember many years ago seeing an article about Josephson junctions. There was a circuit diagram and an arrow that pointed in a direction with a caption "Probability Current". I went, "WHAT?" Then the more I thought about it the cooler it seemed. Now this video completes that for me.
@Culando Жыл бұрын
"By the way it's actually a hundred times more complicated than that" seems to be the motto of Quantum Physics. And the collab with Arvin Ash is awesome! I've checked out a number of his videos too.
@ScienceAsylum Жыл бұрын
Yeah, I think "By the way it's actually a hundred times more complicated than that" pretty much sums up every explanation of quantum physics.
@misterlau5246 Жыл бұрын
The problem is Nick Lucid will have a PhD. And yeah, how can he explain without the fancier stuff? Of course it's complicated, or Nick wouldn't have to study a doctorate to be at maximum of his career
@devarshnayyar3910 Жыл бұрын
This is the equation we all can understand without understanding it.
@Pleasing_view Жыл бұрын
It's just P.E + K.E for subatomic particles. The Science Asylum is just complicating the notion..
@narfwhals7843 Жыл бұрын
@@Pleasing_view it isn't "just" that. It's what happens when you replace the ideas of classical energy with quantum operators.
@Joyexer Жыл бұрын
Trust me... You dont. There are whole research branches dedicated to push this equation to its limits...
@abhishankpaul Жыл бұрын
That moment when you understand that QM can be done but not understood
@oliviervancantfort5327 Жыл бұрын
Actually, you can be in a state of understanding it and in a state of not understanding it at the same time... and you will collapse upon examination.
@Psychx_ Жыл бұрын
I'm from Austria and I'm also a Schrödinger fan. Before the country transitioned to the Euro, the currency was the "Schilling" (read 'sch' in German words as an 'sh' in English, i.e: shilling). The second last iteration of said currency (in the 80's up until the 90's) had Schrödinger and the wave equation on the 1000 bank note. Ofc I had to get one :P It contains a portrait of Schrödinger, the formula symbol of the wave equation and a stilized atom on the front and the main university of Vienna and another stilized atom on the back. For anyone who's into collecting old currencies, I can highly recommend getting one. It's an absolute beauty of a bank note. As a side note, these cannot be exchanged into Euro at the Austrian national bank anymore, but they become increasingly sought after by collectors. If you keep one for 40 years and have it remain in good condition, it may also serve as a nice investment.
@FriedrichHerschel Жыл бұрын
My brother still has a 10 DM bank note, with Gauss on it, for similar reasons. Unlike you, he could exchange it into Euros if he liked.
@MassimoAngotzi Жыл бұрын
Underrated comment. 👍
@Psychx_ Жыл бұрын
@@mal2ksc It's in a superposition of these two states, how fitting :D
@Sanntik Жыл бұрын
I’m sorry to say that “I’m a schrodinger fan” is no longer something you can say, given the controversy around him ^^”
@Psychx_ Жыл бұрын
@@Sanntik Aww, some people on YT/Twitter are offended by a dead person :P I am not bound by cancel culture and it's irrelevant to me whatever he did in his private life, since it's unrelated to his scientic achievements.
@ToriKo_ Жыл бұрын
“The wave equation isn’t about wave shapes, it’s about wave motion” 10:05 great line
@ScienceAsylum Жыл бұрын
Thanks 🤓
@brigittelars5564 Жыл бұрын
But the geometrics of wave motion is also critically important, it can't be overlooked
@AlecBrady Жыл бұрын
This is great! I learned recently (from 3Blue1Brown, actually) that the Fourier transform originated in Fourier's contribution to solving the heat equation, not the wave equation; so the role of Fourier transforms in QM now makes a lot of sense. Thank you for this!
@ScienceAsylum Жыл бұрын
Glad I could help 🙂
@renscience 7 ай бұрын
Fourier’s contribution to the 20th and 21st century is so underrated. Even the uncertainty principle is derived from Fourier. Not surprisingly, as oscillators (everything wiggles ….Feynman) is cosine and sine dependent. And more amazingly, it is all a vector space that can also be tied to linear algebra. A soup all pointing to energy density probabilities… nature is truly amazing
@RalphDratman Жыл бұрын
Yes the Schrodinger equation is first order in time, like the heat equation. But the i factor, by riotating the time derivative by 90 degrees, makes the result very different. In fact, if you split psi into real and imaginary parts, you can write two differential equations, then combine them to finally get a single differential equation that is second order in time. That is, if I remember correctly.
@yvespillot1245 Жыл бұрын
Indeed, you can remove time dependance in schrodinger equation and get the time independent version of schrodinger!
@Camptonweat Жыл бұрын
Yes, I recall the complex diffusion factor is why "probability flow" doesn't have the same broad characteristics as temp flow and can look "wave-y".
@e.b.1115 Жыл бұрын
This. I recall reconfiguring the Schrodinger equation to be second order in time, and the i factor was important
@markcarey67 Жыл бұрын
It depends what the "i"means though - there is an interpretation where time is a clock which is a cycle so anything that describes these kinds of processes at this fundamental level involves clocks diffusing.
@nauy Жыл бұрын
Well, Dirac’s version with second derivative of time (relativistic) got him the Nobel Prize.
@Nexictus Жыл бұрын
I like how he is questioning everything just to explain stuff to us.
@anthonyfaiell3263 Жыл бұрын
Richard Feynman, one of the greatest physicists in the last century believed that the key to truly learning and understanding a concept was to be able to explain it coherently to others in laymen terms. . And just on a general level, intelligent people don't just "have opinions" on things without at least trying to understand them inside and out. So it's likely this was a lot of his actual thought process on working through this. Also, deriving an answer through logic will be much more likely to stick in your memory than deriving an answer through memorization. . In other words, this isn't just for us. He is likely sharing his actual thought process on the matter.
@tf8896 Жыл бұрын
Thanks Nick! This semester I’m taking my first proper rigorous QM class! Perfect timing!
@ScienceAsylum Жыл бұрын
Good luck!
@pinocleen Жыл бұрын
gl hf
@astradrian Жыл бұрын
First-year physics undergrad here and I was just studying these equations! Love your videos Nick; you're one of the reasons I'm studying Physics today ;)
@ScienceAsylum Жыл бұрын
Thanks for sharing. I'm glad I could inspire you 🙂
@ayushaggarwal906 Жыл бұрын
After 4 months I will be studying the same equation.
@Schraiber Жыл бұрын
I actually used the analogy between the Schrodinger equations and diffusion equations (which generalize the heat equation) as the key to my PhD thesis, where I applied path integration methods from QM to population genetics problems that are usually described with diffusion equations
@vikurtz Жыл бұрын
Ooh, has it been published? I'd be interested in reading that
@dimzen5406 Жыл бұрын
I haven't watched you channel for years, and now overwhelmed by all - level of disputed problem, simplisty of explanation, and even an artistic level
@ScienceAsylum Жыл бұрын
Thanks! I've tried to improve a lot over the years.
@SergTTL Жыл бұрын
That boxy wave radiates some old school vibes. A signal from a distant past.
@cdixonweekes Жыл бұрын
Here's the comment I was looking for.
@joepeach997 Жыл бұрын
“Where was I”? My thoughts all through this, and loved every second of it!
@kt420ish Жыл бұрын
Awesome video! Love the colab with Arvin Ash. Both of you guys are amazing at what you do and we as viewers appreciate it
@noahway13 Жыл бұрын
Meh...
@CT-pi2gl Жыл бұрын
Man, what a fantastic summary of some of the main relationships in physics. That free body diagram of the string section related to the equation terms was particularly clarifying.
@ScienceAsylum Жыл бұрын
Thanks. Glad you liked it. 🤓
@macronencer Жыл бұрын
You are brilliant, Nick! Almost every time I watch one of your videos I either learn something new or gain a new perspective. This was really helpful - thanks!
@ScienceAsylum Жыл бұрын
Thanks! Glad you liked it 🤓
@vincentwalker2081 Жыл бұрын
Actually, I watched Arvin last night, February 2, 2023. Thank you for putting it all together.
@dmiller4511 Жыл бұрын
"Curviness determines acceleration" "Probability flows through space" Love these
@brigittelars5564 Жыл бұрын
Just ask this question.. "is probability a physical object? If no then how and where is it flowing? In our heads or in physical cosmos? 😀
@dmiller4511 Жыл бұрын
@@brigittelars5564 Love this. Probability maybe the first step towards a definition of consciousness? Thank you!
@sarthakthememegod Жыл бұрын
Awesome Video as Always Bro! You Make Science so Interesting Thanks a Lot Appreciate it a LOT🔥❤️
@ScienceAsylum Жыл бұрын
Glad you enjoy it! 🤓
@joetedescoyou Жыл бұрын
Thanks for your commitment to lucidity in science.
@ScienceAsylum Жыл бұрын
Thanks for the support!
@punditgi Жыл бұрын
Nick always manages to make these gnarly topics extremely lucid! 😆
@ScienceAsylum Жыл бұрын
Thanks! 🤓
@alexandrebatalha7253 Жыл бұрын
I LOVE your videos, Nick! I'm a physics teacher in high school here in Brazil and always learn and have fun with you! Thanks a lot!! Hugs
@Samien Жыл бұрын
Nice cameo 😎 I have been following both channels for years 👍🏻 excellent as always Nick ❤
@jimmypk1353 Жыл бұрын
Cannot tell you how delighted I am to see the two of you collaborate like this. I took me by surprise. You guys made my day. LOVE YA BOTH! ❤
@ScienceAsylum Жыл бұрын
Our pleasure! 🤓
@hinglish7813 Жыл бұрын
I finally comprehend why the wave equation is written the way it is for the first time. I never really understood the derivation or how to solve it, though we did it. You have incredible aptitude for grasping and communicating physical ideas! The same is true for describing how the probability "flow" in the Schrödinger equation and the heat and fluid equation. I'm so appreciative.
@ScienceAsylum Жыл бұрын
Glad it helped! 🤓
@priyanshumaan8870 Жыл бұрын
nice
@mathadventuress Жыл бұрын
I just took a course on schrodingers equation so this was a treat to watch.
@ScienceAsylum Жыл бұрын
Nice! 👍 I hope this was some good reinforcement.
@daedalus25 Жыл бұрын
As someone with a degree in physics, it always makes me smile when I learn something from the Science Asylum. My undergraduate wave mechanics professor never explained what the Schroedinger wave equation represented. It was just, here it is, now let's do some calculations.
@ScienceAsylum Жыл бұрын
*"It was just, here it is, now let's do some calculations."* Yeah, that's pretty common.
@jacobsvickers3945 Жыл бұрын
Same. Why don't they just say: by the way mathematical abstraction doesn't always translate so we started using probabilities.... Instead they keep it esoteric like it's unbelievably complex and of course it's complex but we already knew that didn't we! It doesn't make Maxwell's equations not true in fact Maxwell's equations account for almost all phenomena except gravity. This is why I decided not to pursue my post-graduate degree in physics seems like a waste to me...
@heavierthanlight7173 Жыл бұрын
Came here from a reference from Arvin... already subscribed long long ago for both. Great teamwork!
@freezinfire Жыл бұрын
It's been so long it seems every time you post a video. Great work as always sir
@carpdog42 Жыл бұрын
I saw both your video and Arvin Ashe's video and decided to watch this first, as soon as you said "restorative force" I suspected there was coordination based on the title of his.
@ScienceAsylum Жыл бұрын
You're a thinker 👍
@gertjan1710 Жыл бұрын
Respect for tackling this. A flow equation instead of a wave equation. Though when you take a time independent solution on a constant potential energy term , you'll get a 'standing (co)sine wave' Which is probably where the confusion originates. As these simpler solutions are always the first ones used in a classroom environment
@sirtajali5841 Жыл бұрын
Thanku 1000 time u have no idea how much your vedios help me. When professors explain schrödinger equation i remain only scratching my had. After watching your vedios my efficiency increase 200%
@cowgomoo444 Жыл бұрын
Interesting video. It did always feel weird to me that it wasn’t a wave equation. But I am slightly confused. Wasn’t Schrödinger motivated by De Broglie’s hypothesis? Namely that electrons were standing waves around the nucleus. That all particles, not just photons, could exhibit particle wave duality. Wasn’t this also used to explain the double slit experiment? I understand that formally it resembles the heat equation, not the wave equation - but wasn’t the whole point to find waves? Even if they are “probability waves” for lack of a better term. I mean I just started studying quantum physics in my undergrad, so I really have very little idea what’s going on.
@ScienceAsylum Жыл бұрын
The "i" in the coefficient on the time side of the equation makes things a bit more complicated (which I glossed over). It allows for rotations in the complex plane and rotations can be viewed as waves if you take a cross-section... but that's two _extra_ levels of abstraction.
@seanspartan2023 Жыл бұрын
I think it all comes down to semantics and something you mentioned on your earlier videos. Namely that quantum particles don't sometimes behave as particles and sometimes as waves, they always behave as particle-waves 100% of the time, i.e. they're something different entirely. It's a shame concepts in physics get mislabeled and the label sticks, but it's a learning opportunity and that's why I appreciate these videos.
@nybble Жыл бұрын
As Feynman once said in one of his lectures: "They do not behave like particles! They do not behave like waves! They behave in their own inimitable way!"
@picobarco4407 Жыл бұрын
@@nybble Yes, I saw that video of Feynmann, it was really cool.
@luudest Жыл бұрын
Thanks for the clarification! I found the term ‚wave equation’ always very confusing: in High School I thought an electromagnetic wave propagates like a water wave through space.
@anthonyfaiell3263 Жыл бұрын
Ah, education. They don't care what you know/think as long as you can regurgitate the exact list of things they fed to you.
@benjamink2398 Жыл бұрын
I mean.... kinda? It does propagate. Through space. And something is waving. Just happens to be the EM field instead of material water
@JivanPal Жыл бұрын
I'm at the 1:00 mark, and my immediate assessment is: The "wave equation" describes a wave that propagates through space over time without its amplitude decaying, whereas the "heat equation" describes the propagation of a property (namely the temperature distribution of a material) over time that does decay over time, namely in an exponential fashion. Quantum wavefunctions behave like that, with their amplitude decaying/spreading out in the same fashion as heat energy dissipates over a material, hence the algebraic similarity to the "heat equation".
@wefinishthisnow3883 Жыл бұрын
Saw you on Arvin's site before seeing your latest upload! Was a nice surprise to see you appear!
@fernandodiazmarin250 11 ай бұрын
I've always thought the "wave" aspect of the Schrödinger was contained inside its use of imaginary and complex numbers, as these are pretty useful for describe some "cyclic" behaviors like the rotational and harmonic phenomena 🤔
@ImDemonAlchemist Жыл бұрын
This channel remains absolutely phenomenal. Great presentaion, interesting and well covered subjects, and entertaining delivery.
@ScienceAsylum Жыл бұрын
Thanks! 🤓
@reinhardtristaneugen9113 Жыл бұрын
Zur Heterogenität dessen, was man nomine so in der Quantenphysik vorfindet: Die Gleichung H Psi (r) = E Psi ( r ) ( das Psi für die Wellenfunktion... ) ist in dieser Form der Schrödinger-Gleichung eine Eigenwertgleichung, wobei ihre Lösungen also Eigenfunktionen zum Eigenwert E ( wer nicht weiß, was das ist, der sich sehe sich die Hauptquantenzahl < n > an... ) sind. Weil die Eigenwertsgleichung meistens nur durch diskrete Eigenwerte in Abhängigkeit der Randbedingungen erfüllt wird, heißen diese quantisiert als Antonym zu kontinuierlich. Ich finde aber das Problem ist, dass, wenn die Leute fragen < quantisiert > was'n das? ...die Antwort < es sind infinitesimale Pakete dessen, was das jeweilige Quant ist, einem zwar Ruhe bringt... ( ...die Leute hauen ab... ...sie hauen aber auch bei🖕ab ), aber keine abstraktionsorientierte Antwort sein kann, weil die Leute autosuggestiv wieder an Teilchen denken und nicht von dieser Anschauung aus dem Mesokosmos wegkommen.. ...Rettung vor dem, was die Sprache der Physik ist, bringt einem eigentlich nur der mathematische Term als Hilfsmittel der Beschreibung aus dem Reservoir, was die Mathematik abstrahiert aufgespannt hat... als letzte Zuflucht für die, die da die Schöpfung so gut wie möglich sehen wollen... ...ich will hier so schnell wie möglich wegkommen!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Le p'tit Daniel🐕🐕🐕🏒🏒🏒
@scottfuller9623 Жыл бұрын
Loved your way of explaining this! Made something very complex seem shockingly simple.
@darkwaveatheist Жыл бұрын
Oh good. A Tuesday rabbit hole to go down with both you and Arvin.
@ScienceAsylum Жыл бұрын
You're welcome 😉
@coloradoing9172 Жыл бұрын
Love your videos, Nick! Keep it up.
@ScienceAsylum Жыл бұрын
Thanks, will do! 🙂
@EnginAtik Жыл бұрын
I've been watching Arvin's and Nick's videos back and forth until Nick's video helped me reach a steady-state.
@Kaiju3301 Жыл бұрын
Don’t be ashamed of plugging your book, it’s a damn good one. I’ve been working through it for fun in my free time which is a lot more than I can say about my copy of Jackson’s e&m book.
@luudest Жыл бұрын
An episode about the History of the Schrödinger Equation would be great!
@araujo_88 Жыл бұрын
Excelent video about the wave equation. Would have helped me a lot when I was taking differential equations lectures in undergrad school.
@deeperblueofficial Жыл бұрын
Props for having Arvin on. I'm a hard guy to make laugh, but this time your law of conversation bit broke me.
@ScienceAsylum Жыл бұрын
You're welcome 😉
@briananderson687 Жыл бұрын
That may have been your best yet thank you!
@digitaldave1576 Жыл бұрын
Keep up the good work, I love your videos
@ScienceAsylum Жыл бұрын
Thanks, will do! 🤓
@Tore_Lund Жыл бұрын
3 equations within the first minute! Love it, this is turning into PBS Spacetime without the beard.
@ScienceAsylum Жыл бұрын
😆
@JustMe-vz3wd Жыл бұрын
Great video explainer. Still the best youtube science channel.
@mikeglover6356 Жыл бұрын
OMG... If I had instructors in my engineering program who had a quantum bit of the talent to explain things so clearly... I would've saved so much head scratching and confusion. Brilliant overview!! Thanks...
@ScienceAsylum Жыл бұрын
I'm so glad you liked it 🙂
@AlipashaSadri Жыл бұрын
at 1:50 , *in general* the horizontal component of the tensions does NOT remain the same after applying the downward force. To keep it the same, you need a very very *soft* string (I am assuming linear-elastic spring behavior) and a very shallow dip (so that cos of the angle is very close to 1)
@zacmilne9423 Жыл бұрын
I just thought of this too
@samarthpatil2053 Жыл бұрын
Very awsm bro Love from India :'))
@thechosenone5644 6 ай бұрын
It took rewatching some parts but the explanations here were great.
@billyyank2198 Жыл бұрын
"Quantum Mechanics is the dreams that stuff is made of." That saying makes even more sense after learning that the Schrodinger Equation is about the flow of probability. Probability, as a quantifiable value, is about as non-tangible as you can get.
@WindsorMason Жыл бұрын
The square wave shown as a "Boxxy wave" is hilarious.
@1002chrisc Жыл бұрын
I love the description of the difference between the broad equation types. Personally, I think of the heat equation in terms of diffusion (mass transfer, but conduction in the heat model). It represents movement across a gradient compared to the beautifully explained wave function's restoration from concavity.
@matthewjackman8410 Жыл бұрын
6:18 Putting Boxxy in the square wave is a very old school internet reference that I am all for!
@jamescomstock7299 Жыл бұрын
Only rarely do I learn something that blows up my mind and lets me emerge with a new, completely altered understanding of our world. This video is one those rare moments and is amazingly the second time you've done that for me. Keep up the amazing job educating us about science!
@Zagneek Жыл бұрын
I struggled with Science at school finding it extremely difficult to grasp. However 40 odd years later I’m finding your vids really fascinating - I won’t pretend I understand the detail but the way you put things across it certainly makes me grasp the overall concepts so cheers for that 😊 One final thought and it might be a daft question but I will ask it anyway: How do we know a particle can be in more than one place at once until we measure it - as the act of measurement will fix it to a particular place, so thefore we can never observe these multiple states? 🤔💭
@lorigulfnoldor2162 Жыл бұрын
Oh, Nick, I once thought of the very same question - "Is this a dissipation equation?" - and asked a physicist about it. The physicist answered that it is not "quite" heat equation because of the imaginary one, the "i"! ("The Imaginary One", now that's something right out from a fantasy book... I mean "imaginary unit", sorry, English isn't my native language). This changes it from dissipation equation to something quite different because every derivative "turns it 90 degrees" in this weird imaginary space. Could you elaborate on this a little? Does it make big enough a difference for it NOT to be a dissipation equation? Or does this only mean that dissipation itself is weird?
@ScienceAsylum Жыл бұрын
I'll admit the "i" in the coefficient muddles things. You could argue that Schrodinger's equation is really it's own thing.
@JaskoonerSingh Жыл бұрын
One of your best vids yet.
@ScienceAsylum Жыл бұрын
Thanks! 🤓
@moreaufamily437 Жыл бұрын
PDE's a favorite topic of mine. Very well done!
@ScienceAsylum Жыл бұрын
Thanks! 🤓
@MurseSamson Жыл бұрын
You know, I actually got a lot from this video. Thank you Nick for clarifying the perspective of the *wave* and *flow* itself. Arvin also has some great videos and I've watched nearly all of those too. Thank you both very much for making these videos! ♥️🙏 I look forward to reading your *Fine Structure* education!! Thank you so much!
@ObsessiveClarity Жыл бұрын
This is awesome! The only thing swept under the rug is that Ψ isn't a pdf, but a complex number, and |Ψ|^2 is a pdf. So it's not probability that is flowing but something very closely related. An intuitive explanation of the meaning of Ψ would be incredible
@ScienceAsylum Жыл бұрын
Unfortunately, we don't have a physical interpretation of Ψ because we've never observed it directly.
@TooSlowTube Жыл бұрын
@@ScienceAsylum Are there any other links between quantum mechanics and thermodynamics? They both seem to be describing something statistical - lots of little tiny things, running around and interacting with each other on a scale that's too small to follow the details, so we are only really aware of a summary (averages and distributions) of what happens, not so much the details of individual interactions.
@richardspectacular5327 Жыл бұрын
@@TooSlowTube look into statistical mechanics and quantum decoherence. Have fun going down the rabbit hole, see you on the other side!
@brigittelars5564 Жыл бұрын
@@ScienceAsylum so in place of the real physical thing, humans just plug in probability which is not also a physical thing, right?
@combcomclrlsr Жыл бұрын
Okay. This is like the best explanation I've seen.
Жыл бұрын
The best explanation of the wave equation ever seen. This intuitive approach to the meaning of the second derivatives with respect to time (acceleration) and space (curvature) is needed to a full understanding of the equation, but almost never explained. You are the best in clarifying physics equations!!
@ScienceAsylum Жыл бұрын
Thanks! Honestly, I (partly) regret putting it inside a video about Schrodinger's equation. It should have been its own 5 minute video.
Жыл бұрын
@@ScienceAsylum But you can make another video about waves and repeat it with other things. I suppose that is hard to find a different subject of physics every week. Doesn't matter to make several videos about the same subject. It is usually made with special relativity, but it can be made with everything.
@pesimeon Жыл бұрын
Great! This video leads nicely into a discussion of the epistemic vs. ontic nature of the wavefunction.
@Mysoi123 Жыл бұрын
Turn out seeing Arvin and Science Asylum both uploaded at the same time is not a coincidence! 😭😭😂
@ScienceAsylum Жыл бұрын
Nope! Not a coincidence.
@grapy83 Жыл бұрын
Excellent video... As usual. Thank You!
@esquilax5563 Жыл бұрын
I thought I understood this stuff pretty well, but your videos consistently blow my mind!
@ScienceAsylum Жыл бұрын
Thanks!
@TheHumanHades Жыл бұрын
That was really very exciting and eye-opening. Thanks Nick 😃
@gretchenchristophel1169 Жыл бұрын
I love your videos...even if I only get half of what you're talking about 🤣 Yet...at the end of your videos I feel like "I got this". Feel smart for about 20 minutes 😂 Seriously...I love physics and even though I could never be a physicist there's just something about the science that tweaks my brain. Thanks for making a tough (for me) subject enjoyable.
@keepmoving1185 Жыл бұрын
Great work as always my friend
@ScienceAsylum Жыл бұрын
Thanks! 🤓
@12kenbutsuri Жыл бұрын
Amazing explanation!
@sslelgamal5206 Жыл бұрын
I loved it, thinking about Schrodinger's equation as heat dissipation equation was fun! 👌👌👍👍 Well I think the comment about three types of equations in classical physics is correct if we change the "type" with 'category"! Most of physics equations are of order 2 and linear with constant coefficients mostly, when working with second order differential equations, we only have hyperbolic, parabolic and elliptic variations (discarding the degenerate cases).
@obi6822 Жыл бұрын
The classification "elliptic, parabolic, hyperbolic" is complete only in 2 spatial dimensions.
@anon2497 Жыл бұрын
Since I can't give two thumbs up for your second order content, I leave this comment in its place. Two thumbs up man! Keep making this amazing content! You are one of my favorite science communicators, and easily one of the most entertaining while also maintaining an incredible fidelity! (Ps: I only said "one of" because I don't want the other kids to get jealous, but between you and me? We know who my favorite actually is, right? Wink wink...)
@randyscott709 Жыл бұрын
Thanks for again making us stretch!
@tommywhite3545 Жыл бұрын
To me the videos you make with humor and/or describing the equations (math) with simple words, instead of leaving them out completely, are your best ones.👍 (I think most people just want to know what the equations come to anyway, without studying mathematics.)
@ScienceAsylum Жыл бұрын
Thanks Tommy!
@kentjohnduga6833 Жыл бұрын
This is a great intro to understanding the Schrodinger Equation! And this is also what my research professor taught me on how to view the equation: you can recast the Schrodinger Equation such that it can be explicitly shown that it is indeed a continuity (or a flow) equation in which Probability Density is conserved and a so called "Probability Current Density" carries the flow. Think of it as if there is no current, then the probability won't change; similar to when there is no flow of fluid, there will be no change in the accumulation of fluid. After all, the Schrodinger Equation enshrines the Unitarity Principle. Anyway, my comment I guess is about the notion that Schrodinger Equation is a derived equation. Here, it is said that it was derived from Conservation of Energy. But my Prof always says (I am in his Quantum Foundations theory group btw) that Schrodinger Equation cannot be derived. It is a conclusion of a concoction of several experiments and postulates. It just so happen that the Schrodinger Equation fits snugly in our current view of Physics such that one could say that it could be derived from say the Conservation of Energy. But with the same logic, Schrodinger Equation could also be "derived" from a proper Lagrangian Density and from the Hamilton-Jacobi Equation, among others, which stems from the fact that there is a symmetric transformation that gives rise to a conservative quantity. Hence, you cannot pin-point where it really came from. He always corrects me: "You cannot derive the Schrodinger Equation: it is a result of many experiments trying to describe our weird nature." Still this is a great video and I learned a lot! Thank you!
@screenaccount2894 Жыл бұрын
Every wave equation implies a continuity equation.
@vfa.vinicius Жыл бұрын
If the Schrodinger equation is a diffusion equation, then it has an imaginary diffusion coefficient, which in turn makes it weird to call it a "diffusion equation". I mean, the "i" in the Schrodinger equation makes a big difference... Because of the "i", the solutions must be complex, and the equation has U(1) phase invariance, which leads to conservation of probability in QM. None of that is true for the heat equation with a real diffusion coefficient, because there's no phase invariance and no conserved quantity. As similar as these two equations may seem, the "i" introduces some properties to the Schrodinger equation that are just not present in the diffusion equation.
@ScienceAsylum Жыл бұрын
Sure, it might be better just to label it it's own unique thing 🤷♂️
@zetacrucis681 Жыл бұрын
Pedantic me says it's a diffusion equation of which the heat equation is a special case. Whether it is also a kind of wave equation depends who you ask but diffusion waves are definitely a thing. Fun video from Nick as always.
@dragonbmgo Ай бұрын
Man.. I love these kinds of videos ♥︎
@thedeemon Жыл бұрын
But it does relate "curviness" (in complex phase) to oscillation! The stronger WF spirals in complex plane, the faster its amplitude changes, the faster it "moves" through space. And for free particles this function does look like a wave with all the wavy properties. Nice visualisation here: kzfaq.info/get/bejne/gsCZmJWCqJuukpc.html
@itskelvinn Жыл бұрын
Everyone remember that it’s ok to be a little crazy
@spitsmuis4772 Жыл бұрын
7:32 Every 100 videos on a subject you will find something truly enlightening that you will remember forever
@jasoncassibry Жыл бұрын
This video was excellent. And I must add that whomever the musician was playing jaw harp sounds at 7:57 is world class. 😅😂
@hakanegne Жыл бұрын
in my opinion, the term of "wave-particle duality" is wrong. The right term must be "vortex-particle duality"..
@john-or9cf Жыл бұрын
Somehow my highly paid professors half a century ago failed to make this as clear as you have…🤓
@AnonymousAlcoholic772 Жыл бұрын
Probably your best episode.
@ScienceAsylum Жыл бұрын
Thanks!
@BlueGiant69202 Жыл бұрын
Excellent video! The way you brought Arvin Ash in was very smooth! Is this the start of a beautiful dynamics duo? While I was listening, I was reminded of John N. Shive's 1982 book , "Similarities in Physics" and Nelson Stochastic Mechanics.
@marceljanssens5935 Жыл бұрын
Didn't you kind of gloss over the i on the right-hand side? Since the solution is a complex power of e, multiplying by i is kinda-sorta taking another derivative. So, the right-hand side behaves second-derivativy.. So, that's still kinda wavy?
@ScienceAsylum Жыл бұрын
But it's an _abstract_ kind of wavy, and more of a rotation than a wave.
@yvespillot1245 Жыл бұрын
Technically, the real and imaginary parts of the waves function are waving and behave like waves. So isn't schrodinger something more in between? Otherwise very nice video about wave equations, it really raised my intuition level
@ScienceAsylum Жыл бұрын
I'll admit the "i" in the coefficient muddles things. You could argue that Schrodinger's equation is really it's own thing. (But yeah, the Schrodinger stuff was just a way to talk about the wave equation without boring people. This video is about the wave equation.)
@romanieo Жыл бұрын
Sweet Lord this was great and extremely helpful Nick. You and AA are connecting the disparate dots into a cohesive whole.
@ScienceAsylum Жыл бұрын
Thanks! 🤓
@BitJam Жыл бұрын
The Schrödinger equation (SE) is technically a parabolic equation (PE), also known as the parabolic wave equation. This is an excellent approximation to the full wave equation when the motion is primarily in one direction. The approximation in the SE is that particles are only moving forward in time, in other words: non-relativistic. IMO it is rather silly to claim PEs are not wave equations (in their applicable domain) since they give solutions that are extremely close to those of the full wave equation. For example a PE equation is routinely used to calculate how sound waves propagate thousands of miles in the ocean. The "waviness" in the SE is in time, not necessarily in space. The eigenfunctions typically have a factor of e^-iEt which contains the waviness. It is no surprise that when you ignore these factors, the waviness goes away. Stanley Flatté published an excellent pedagogical article that shows the relationship between the SE and the full wave equation (Klein-Gorden equation): The Schrödinger equation in classical physics American Journal of Physics, Volume 54, Issue 12, pp. 1088-1092 (1986).
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