Don't forget to check out Arvin Ash's video on the ubiquitous harmonic oscillator: kzread.info/dash/bejne/dI6G2JqHm9KfiLQ.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."

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.

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...

"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

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.

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.

“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

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

6 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

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.

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

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.

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

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.

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. 🤓

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.

“Where was I”? My thoughts all through this, and loved every second of it!

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 🤓

Thanks for your commitment to lucidity in science.

@ScienceAsylum

Жыл бұрын

Thanks for the support!

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...

"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!

Nick always manages to make these gnarly topics extremely lucid! 😆

@ScienceAsylum

Жыл бұрын

Thanks! 🤓

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! 🤓

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 👍

Actually, I watched Arvin last night, February 2, 2023. Thank you for putting it all together.

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

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...

Awesome Video as Always Bro! You Make Science so Interesting Thanks a Lot Appreciate it a LOT🔥❤️

@ScienceAsylum

Жыл бұрын

Glad you enjoy it! 🤓

Loved your way of explaining this! Made something very complex seem shockingly simple.

Nice cameo 😎 I have been following both channels for years 👍🏻 excellent as always Nick ❤

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.

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

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.

It's been so long it seems every time you post a video. Great work as always sir

Love your videos, Nick! Keep it up.

@ScienceAsylum

Жыл бұрын

Thanks, will do! 🙂

Saw you on Arvin's site before seeing your latest upload! Was a nice surprise to see you appear!

Came here from a reference from Arvin... already subscribed long long ago for both. Great teamwork!

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

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.

That may have been your best yet thank you!

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!

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

Excelent video about the wave equation. Would have helped me a lot when I was taking differential equations lectures in undergrad school.

It took rewatching some parts but the explanations here were great.

I've been watching Arvin's and Nick's videos back and forth until Nick's video helped me reach a steady-state.

This channel remains absolutely phenomenal. Great presentaion, interesting and well covered subjects, and entertaining delivery.

@ScienceAsylum

Жыл бұрын

Thanks! 🤓

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.

Great video. I am fascinated by wave & heat equations for a long time but haven't look at it from this angle yet. They are super easy to understand using grid based simulations. One grid for the wave height (concavity in the video) and one for velocity. All the scary looking derivatives just turn into simple subtraction. Totally worth a look into it.

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".

Keep up the good work, I love your videos

@ScienceAsylum

Жыл бұрын

Thanks, will do! 🤓

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.

Great work as always my friend

@ScienceAsylum

Жыл бұрын

Thanks! 🤓

I thought I understood this stuff pretty well, but your videos consistently blow my mind!

@ScienceAsylum

Жыл бұрын

Thanks!

3 equations within the first minute! Love it, this is turning into PBS Spacetime without the beard.

@ScienceAsylum

Жыл 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 🤔

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 😉

Okay. This is like the best explanation I've seen.

An episode about the History of the Schrödinger Equation would be great!

Oh good. A Tuesday rabbit hole to go down with both you and Arvin.

@ScienceAsylum

Жыл бұрын

You're welcome 😉

Thanks for again making us stretch!

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.

11 ай 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.

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? 🤔💭

Very awsm bro Love from India :'))

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%

It's huge! The book that is. Looking forward to having time to read it! 😊

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

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?

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.

One of your best vids yet.

@ScienceAsylum

Жыл бұрын

Thanks! 🤓

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!

Great! This video leads nicely into a discussion of the epistemic vs. ontic nature of the wavefunction.

wow, so many patterns in such a simple equation, you're my hero!

Excellent video... As usual. Thank You!

The square wave shown as a "Boxxy wave" is hilarious.

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.

Amazing explanation!

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).

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.

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...)

This video was excellent. I immediately went to look up the Black-Scholes equation as I had remembered it had been derived from the Brownian heat equations. In that equation (at least for European options) we see a first order term for time and a second order term for motion. This video has revealed a relationship that I had never connected before. It is like a curtain has been lifted. Thank you!

@thedeemon

Жыл бұрын

This vid completely ignores the fact we're dealing with complex numbers here, and the way curviness in complex phase influences amplitude makes it very different from ordinary heat equation where all numbers are real, not complex.

gold gold gold. Thank you for this amazing content!

That was really very exciting and eye-opening. Thanks Nick 😃

Turn out seeing Arvin and Science Asylum both uploaded at the same time is not a coincidence! 😭😭😂

@ScienceAsylum

Жыл бұрын

Nope! Not a coincidence.

Outstanding. As always.

PDE's a favorite topic of mine. Very well done!

@ScienceAsylum

Жыл бұрын

Thanks! 🤓

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.

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.

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 🙂

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!

Everyone remember that it’s ok to be a little crazy

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.)

Man...that's really a perfect timing...I have engineering physics exam Tomorrow and I have searched many videos....but your video made me a clear mind of seeing equations 🙂🙂

Great video explainer. Still the best youtube science channel.

Somehow my highly paid professors half a century ago failed to make this as clear as you have…🤓

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 🤷‍♂️

Yes i will check out Arvin's video after.

Holy moly! Awesome video! 🎉

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: kzread.info/dash/bejne/fo6dx5SKc5iwksY.html

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.

Amazing, like always!

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 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 was'n das? ...die Antwort Le p'tit Daniel🐕🐕🐕🏒🏒🏒