I think it's really a testament to your explanation skills that the Schrodinger equation seems like it's the obvious solution once you've seen it. It was, of course, not obvious, even to Schrodinger himself. The time and effort you must put into these videos is astounding, and I thoroughly enjoy watching them. Great work!

Having taken a physics degree many decades ago may I congratulate you on such an excellent presentation.

In all of my university courses, textbooks, websites, and videos I've indulged to learn intro QM, this is easily the best overview with the clearest and most well-put explanations and motivations. Thank you.

I love how you start building up from the historical background, something we don’t see often. I hope you will upload more often❤️

I've spent the last few days watching through this and filling up over 25 pages with notes. I would always pause and see if I could derive/solve the problems every time. I would get stuck about half the time and when I caved and watched your walkthrough I would frequently be like "You can do that?!?!?! No way!!". Watching the solutions to the time independent schrodinger equation match up with my undergrad chemistry education was such a mind blowing moment. When I finally understood why energy was quantized was a big aha moment for me. But then when you pulled up the graph of the energy levels in the box and the probability distributions, I flipped out. What an amazing video. I cannot thank you enough for this amazing content. I can't wait to watch every video on your channel many times over.

It always amazed me, that when I was in school everything about quantum mechanics was a synonym of something very difficult and counterintuitive, thanks to the pop culture and popular science articles/videos on youtube. After studying in university it turned out to be much easier, espesially considering that classcial mechanics is not that simple either. If i saw this video 5 years ago I would have understood that fact earlier. Thank you for this clear and neat explonation.

Watching your content is like watching a new lemmino video for me; an absolute treat!

Outstanding work. I somehow managed to understand all of it, whilst understanding none of it at each stage. Coming from a non-physics background, and with only a limited understanding of calculus, to be able to carry a viewer with my limited ability along is testament to your superb communication. Thank you.

Bro. Wtf I love you. This was the best explanation of ANYTHING I've ever seen. It's so freaking intuitive I'm actually flabbergasted. Without a doubt, the world is a better place because of people like you. There's so many videos on KZfaq about the Schrödinger equation and quantum mechanics in general. I've watched so many, and none of them capture it like you do in this video. Truly, you are the best teacher I've ever watched on KZfaq--and I've watched an unhealthy amount of educational KZfaq videos. Like Walter Lewin level. BUT BETTER. Omg I can go on and on. Never understood differential equations or partial differential equations before... now I feel like I can approach those topics by myself. You literally explained why quantum mechanics can be ignored in classical systems because they have large amounts of energy, which make the probability distribution indistinguishable with our instruments. And you did this as an aside. Like I'm halfway through the video and so excited to keep watching. Kudos dude.

For unexpected reasons I’ve been confined to a hospital bed for the last few days. This video was a ray of sunshine, distracting me with an hour of exciting, challenging material. You’ve earned yourself a new patron. 👍🏼

I am doing my doctorate in Engineering, and studying theoretical physics is my all time favourite hobby. I am going to derive all these myself now. Many thanks for creating this wonderful presentation.

What I like the most about this video is that he always kept the proper math behind the theory, and all the simplifications/interpretations are clearly justified. Most KZfaq videos on quantum mechanics don't go this deep into the math, so many things like the probability interpretation of the wave function become vague. This video does a great job to fix this. I think that any Freshman with a little bit of calculus background can understand what is going on in this video.

Man, you should be given a Nobel prize for putting this all together. Very good explanation!

you did a great job. Nine out of ten physics professors today just brings out the " Schrödinger equation", on board. This is exactly how the Quantum Physics was taught in 1950s, 60s, 80s, 80s, then all on keyboard now.

A masterpiece of outreach science work There has clearly been so much work gone into this, on every level:- academic, planning, scripting, visual representation and presentatuon. Simply superb. Thank you. Thank you. Thank you!

One of the best Physics KZfaq channels, probably top 2 or 3 in my opinion.

I cannot express how incredible this video is. Thank you so much for the work you do, I've never seen anyone on KZfaq deliver the _intuition_ behind the theory, both the derivation of the maths as well as the implications and applications of said math on physical results. And to do it in such a clear and concise way that you can follow along step by step, it really is an impressive feat. I also really appreciate the history of how these theories came to be, it is such an important part of physics that often gets left out when it has an entire story to tell. Cheers mate.

I particularly love 33:10 where, without even applying the equation to the real world, the math just collapses into giving such a clean an interpretable result for K. Blew my mind.

After a decade I can understand the formulation and intuition behind the Schrodinger wave equation and brother this is the most phenomenal work and explanation I have got till now I paused the video in between just to say thankyou for your work and effort.and thanks to the technology so this information could be shared across the continent

I just recently watched a video on the Schroedinger equation from another channel, and it made a much bigger assumption in the derivativation and it felt unmotivated. The beginning of this video really helped me feel like the equation makes sense.

It is truly remarkable your mastery over the subject and ability to express it so lucidly. Well you have cleared many of my doubts in quantum physics and probability theory. Specially why imaginary 'i' is present in quantum mechanics and how quantum physics explains the behavior of classical physics too. It is true we just need quantum physics to explain the world around us. There are no words to express my happiness, when I watch your videos. Looking forward to video on deep dive into Schrodinger Equation. Thank You!

I made a 30 page notes watching this entire video to delve into the world of quantum mechanics! Believe me, my thinking frame has changed a lot in QM upon completion this video. Thank you for this knowledge!

I have a theoretical degree in Physics, and I gotta say, you did a good job presenting this equimation.

Best explanation ever, better than any of the textbooks out there; you explain it better than any professors I've ever encountered.

Every time I watch one of your videos I am struck by the extreme quality of your explanations and your ability to make the material accessible to those of us without a long formal education. Thank you for all the time and efforts that have gone into producing these videos!

Even though the video is 1,5 hours long, I still had to pause every 30 seconds because it was going too fast for my brain. Really helpful video, 10/10!

for a lay person that is interested in science and physics, this is a great explanation of something I have struggled with for years

This video squeezed all of the Physics out of the infinite square well! Nice! The time-independent, one-dimensional Schrödinger Equation is an example of a Sturm-Liouville differential equation, in which the concepts of eigenfunctions, eigenvalues, orthogonality, completeness, etc. are developed in the general case; these concepts are also expressed in the context of Linear Algebra. The mathematics of symmetry (Group Theory) constrain the allowed transitions between different states. The Mathematics of Quantum Mechanics is simpler than the Physics of Quantum Mechanics. One can grind through the demanding computations, but the physical comprehension is still challenging: "What is happening between the states?"

Just the perfect amount of details. The depth and breadth of these videos are fantastic, thank you for putting all this effort into them!

My first time Kayaking and this Kayak held strong. kzfaq.infoUgkx4k5UrhC3v_Y4hIEaXLGvHcN5a5aBmZNB The water got pretty rough as a speed boat zipped by me, and the Kayak withstood it (I expected to be capsized). The Ores are very easy to put together, the pump worked beautifully. the seats are a bit hard to sit in after a while (I recommend sitting on the floor). after reading the reviews I was very scared it'd get a hole in it, the material is very strong and durable. The Air valve may need a small Phillips head screwdriver to adjust, other than that, it's well worth the money!(update)I've gone Kayaking in 3 Lakes and 2 rivers totaling about 40 miles. the kayak had two holes and they patched easily and no other problems can't wait for kayaking season this year!

This video starts with an excellent overview of Schrödinger´s life. Then his unitary evolution equation is presented. Congratulations to the authors. For those already initiated in QM I repeat here some comments previously made to similar videos. They may clarify debatable points. The Schrödinger time dependent equation (STDE) when applied to a wave representing an initial state of, say, an electron bound to a proton and together forming a hydrogen atom, predicts and retrodicts all the future and previous states of the electron wave, in the same fashion than the evolution equations of classical mechanics predicts the movement of the Earth around the Sun. Note that the STDE is energy conservative, that is, the initial state as well as the predicted and retrodicted ones all have the same energy. As is well known the bound electron has a completely different conduct. Whatever the initial state and in absence of other interactions an excited electron will settle in a stationary state radiating energy (in the form of a photon) along the way. If the stationary state is the ground state the electron will stay there forever (in absence, as said before, of other interactions). Otherwise the stationary electron state is ephemeral and will be abandoned to radiate a photon and assume a new stationary state of even lower energy. This "down the staircase" process repeats until the ground state is reached. There is no manner to adapt the STDE to this physical process. This inconsistency was discovered by none other than Niels Bohr, as can be inferred from the report of Werner Heisenberg. See our note www.researchgate.net/publication/356193279_Deconstruction_of_Quantum_Wave_Mechanics After discovering the tremendous inconsistency it would have been natural to announce that the STDE contradicted with physical facts, and ask for a correct equation. I assume as true, but only know from hearsay very long ago, that in Einstein's viewpoint the correct deterministic time dependent wave equation had to be non-linear. References to this historical detail would be appreciated. It is hard to believe but, against reasonableness and common sense, Bohr decided to adopt the STDE as correct and that continuity, causality and determinism of physical processes were wrong because they contradicted the STDE. Apparently mathematical equations on paper were more relevant than the experience of the whole human race. Then a series of new and fanciful "quantum physical principles" were adopted. In my opinion the powerful quantum establishment dogmatically defends Quantism and strongly rejects any attempt to correct its misdeeds, even if the correct deterministic time dependent wave equation available. With best regards to all. Daniel Crespin

This is hands down the best explanation of the Schrodinger eqn. I have ever listened to. You answered all my questions about it that my professors and other videos weren't completely answering. Thank you for putting in so much time and effort into making this. I finally understand.

6:23 Generally speaking solutions to second order partial differential equations of this form will be sine or cosine functions, as well as exponentials. Which makes sense since sine and cosine can be written in terms of exponentials, and exponentials can be written in terms of sines or cosines. That means that if one type of function is a solution to an equation, then so is the other. 8:02 If you are new to physics and are not sure why the relationship in the equation is true, here is a simple explanation. Frequency is nothing more than a count of the number of waves that pass a point in one second. If you stand on a dock and count the number of waves striking the dock in one second you have the frequency. The wavelength is the length of one complete eave, an easy way to measure it is to measure the distance from the crest (peak or highest point) of one wave to the crest of the next. With the terms defined, here is a simple analogy I used to teach this. Imagine two lanes of cars driving along a highway at 60 MPH. You stand at the side of the highway and watch. The cars in the lane closest to you are well behaved drivers and are separated by six car lengths. The drivers in the next lane over are separated by only three car lengths, or half the distance of the cars in the first lane. The distance from car to the next will represent the wavelength. It should be obvious that in any given time twice as many cars will pass you in the far lane where the distance between them (wavelength) is half the distance (wavelength) of the cars in the near lane. In other words, when we decrease the distance the number of cars (frequency) increases. Cut the distance in half and the number of cars (frequency) passing you doubles. It is an inverse relationship, meaning one variable decreases by the same factor the other increases. 9:13 Those two equations are exactly the same except they are written with different variables. A little algebra allows you to transform one into the other. 13:53 hf = E on the right side. On the left side he substituted p = h/lambda in the p^2/2m term for kinetic energy.

I hope you know this video came at the perfect time for me. Ive been teaching myself quantum chemistry from a physical chemistry textbook recently and i was using your channel to understand blackbody radiation haha. Glad to see a new video from you man! You always put in an insane amount of time into these

I'm going to take like 6 weeks to review Calculus again and come back to this one. And I don't mean that sarcastically! Your videos really inspire me to take topics seriously which I got C's in school. These are great videos, there are just some parts in the solving of the schrodinger equation section that I'm having to pause for a long time to be able to process. But please don't take that as a request to simplify your videos. It would be a disservice to this equation to not get so into the maths of it. Your method of explanation is still the best on youtube.

Great work in explaining the equation. Having an undergraduate degree in engineering is enough to follow the video in every step of the way. Thank you very much.

cant believe you came back with this absolute 90 minute banger. your work always inspires me to keep studying and it keeps me motivated

I wish i clicked on this earlier, im about to fall asleep, but i can tell that this video is very thorough and deserves my full attention when i can give it. In any event you gained a subscriber, i thought i was subscribed already, but i genuinely appreciate the level of effort and clear passion that goes into your explanations

1978, Freshman Chemistry day 1, possibly my very first class at Caltech: The professor gets up in front of the class and writes Shrodinger's equation on the blackboard. Remember, we are all Freshman. We have not ever seen a partial differential equation before in our lives. My first thought was 'What the hell have I gotten myself into?' Turns out that that was one of my easiest classes lol. Practically our entire first trimester in chemistry was spent dealing with Shrodinger's Equation.

This was a beautiful description that delved into the shrodinger equation without making it seem like a unbreachable concept. This is exactly the introduction I've wanted

Thank you very much for the simple derivation. Literally every Schrodinger Equation video I watch just explains what it is without deriving it. Total Energy (Hamiltonian) = Potential Energy + Kinetic Energy. Yes yes yes, but how did he COME UP with it? To which I was told he just conjured it up out of his rear end, because that's his genius (facepalm).

Wow! Excellent video and explanation. I wish this video had been available back in 1986 when I took a class in "Modern Physics" as part of my electrical engineering degree. I appreciate the effort you put into this.

Today’s generation is so lucky to have these types of videos. Your step-by-step methodical derivation answers so many questions for students just starting out…, I just wanna say thanks. Absolutely brilliant. Definitely the best video on the topic by far.

BEAUTIFUL!!! Just barely starting to get the grasp of it and you're the one whose giving me the motivation to study physics. Thank you so very much!

Brilliant explanation.There is so much content squeezed into this single lecture.

You had me two days ago. I hope it stays on schedule this time around.

I love how you mention that this is a brief explanation of Schrödinger's Equation, and it's an hour long video

When we had to study quantum mechanics in university (albeit only at surface level) it was presented as merely factual. The way you put it in historical context as something being derived from classical mechanics with its secrets and deeper meanings slowly being uncovered, somehow makes it much more understable. Thank you! I was slightly dissapointed by the lack of cats in your video 😁

You are one of best teacher, I've ever known. Feynman was famous for his teaching ability, i don't know him much. But you have made me understood physics at a different level, so thanks a ton for your videos 👌👌👌

Having a brief stint as a college lecturer myself, I can clearly see the passion you have for physics. Your simplicity of presentation and yet, not giving up on the rigor is just too good. Schrodinger's wave equation (I wish we had these kinds of videos back in our college days) was one of those toughest topics I couldn't grasp, but knew it was definitely something. One of my professors spent a lot of time explaining to me, but alas, sometimes it takes time for things to percolate 🙂!! Good job my friend !

You are a gift. The transformation of the complex to a simpler state of comprehension. Yes, you are gifted; but you are a gift to the rest of us. Incredible video.

I saw the video, dropped everything and got the popcorn...that's how good they are. I will now place myself in a 1 dimensional well with infinite potential up and out for the next 90 mins. Hope the new job won't throttle the channel's content.

I’m a 1st year engineering student, and while I do enjoy my course my real passion lies with physics. These type of videos are perfect for exploring that using the foundations I have learned studying and I couldn’t be more grateful.

Massively excited for the new content. Everyone of your videos is a treat for the mind. Cheers!

By far one of the best materials concerning the basics of quantum mechanics on KZfaq. Thanks for that, I feel privileged to have had this video as my very first approach on the subject, certainly other sources would confuse me a lot more, what didn't happen on the last 1h27min. Congratulations!👏👏👏

I have never heard anyone explained the schrodinger equation as clear and concise as you are.

Beautifully explained! What a great refresher of QM with valuable illustrations

Only 20 minutes in and this answered so many questions that I never know how to ask during my physics degree. Absolutely incredible, better than some professors

Excellent. I wish this was available 30 years ago when I took physical chemistry.

YOU ARE AMAZING!!! this is much better intro than any of the physics textbooks could offer me...

Well done! Congratulations. As a composer/librettist, I have been pursuing the transition of one vibrational mode to another for most of my life and am convinced vibrational resonance is the essential component of not only matter, but the entirety of the cosmos.

Granted, I haven't had the time to watch the whole video at this point, but I'd still like to write this down before I forget it, in case some future reader will find the idea interesting. As it happens, when looking at things at a more fundamental level, one needn't postulate the form of the Schrodinger equation for a general potential. The equation itself follows from the deeper assumption that the canonical structure of Hamiltonian mechanics is preserved when going from the classical realm into the quantum one. Following with the appropriate expressions for the generators of transformations (such as translations, rotations, time evolution) and the commutation relations for operators associated to observables that preserve this structure, one ends up with the general differential equation of the time evolution operator itself in terms of a Hamiltonian operator reminiscent of the Hamiltonian functions found in classical dynamics. From there on it follows immediately that the Schrodinger equation in the form presented here holds in any Hilbert space, be it one of abstract state vectors or a representation in terms of coordinates or momenta, for an arbitrary potential operator. Equivalently, one can set up a more general version of Hamilton's principle, the so-called path integral formulation of quantum mechanics due to Richard Feynman, which culminates in the same result for the equation of motion. It is also worthwhile to note that the Schrodinger equation treats only the dynamics of the particle as "quantum". Fields introduced via potential operators are still classical in nature, and this discrepancy leads to some of the "weirdness" of non-relativistic quantum mechanics. For example, the non-local nature that appears in the non-relativistic treatment of phenomena such as the Aharonov-Bohm effect vanishes when the field itself is also quantized.

Bro, Watching your video is relaxing as heck. I watched this in several parts over few days. Now, I will rewatch it soon and also explain to my school students, lol.

Thank you so much on this video!!! In the past I only knew these concepts as separate themes like the Heisenburg's uncertainty principle, but I've never seen them connected together in SUCH an ELEGANT way. THANK YOU!

Thanks a lot for making this knowledge so accesible. I had recently read an non-technical book about quantum physics, and I was curious to understand how the math worked out. Your explanations are so well-derived, built with so much patience. Thank you again :)

That is the clearest introductory video about this subject I've ever seen. 👏👏 I'm very excited for the next video

One of best and most lucid explanations of the Schrodinger equation I have come across. I would like to see you do a full course on QM! Excellent work!

I remember when I first started following this series on the quantum world a while back. I could tell from the first video that it was going to be great, and this just proves all of it! Thanks so much for putting these together. If could make a request, can you please make a video (or a few if required) to explain the wave functions of boson and fermions? The Pauli exclusion principle comes out of this, and basically everything we would call "structure" in the world comes out of that, so I think it would be fascinating! Edit: There are plenty of people on YT talking about the weirdness of QM, but not so many talking about the fundamentalness of it. If it were not for antisymmetric wave functions and fermions, the world as we know it would not exist. That is where "normal" begins. I think that is far more relevant than any strangeness. Keep on keeping on friend! Great videos!

I love the way you explain difficult topics. It makes physics look easier. Edit:Can you do a video on tensors and Einstein field equation?

Very good. When we were taught quantum mechanics, it was a, "Don't bother where Schrodinger's equation comes from, here is how to use it" approach. I much prefer a historical approach such as this so that the equation is put into context.

I have seen a few of your videos now and I just love them. You are great. I have a PhD in fusion plasma physics and my expertise is magnetized plasma but I have studied QM, GR, etc a bit in my life out of curiosity. I believe your videos can be seen by pretty much anyone with an interest in physics regardless of prior knowledge, except of course they need to know a bit of math. But if they are interested in physics it is very likely that they do know this little bit of math.

Absolutely the best lecture on Schrodinger equation. You won my respect with my full heart. Thank you so much!

I never attended college and self-taught rudimentary integral and differential calculus. Some of the symbols and techniques on display are a bit foreign, but allows me to feel unintimidated when you do the heavy lifting off-screen as I can recognise the correlations. Finally! I have a semblance of an answer to question that's bugged me for decades: WTF is a wave function? Also, seeing i being introduced in the theory then wiped out in the practical is deeply satisfying.

Wonderful ! Once you have made an equation clear, it becomes absurdly simple! What a brilliant way of explaining! Hoping for more videos and thank you for saving my time on searching for a better explanation through the internet!❤😊

Thank you for your excellent and very clear explanation. I appreciate the hard work put into the video. When I was in university, my lecturers wasn't even a fraction as clear and enthusiastic as you. Well done!

was wondering when you’re next video would be, couldn’t believe it when I saw it was an hour and a half! Videos like these are a gift, thank you!

I think you have done an excellent high level analysis of this. As you clearly know, Schrodinger had the edifice of the Heisenberg-Born-Jordan matrix mechanics model to deal with as well as the de Broglie wave perspective. Schrodinger proved the equivalence of the matrix and wave perspectives in 1926. This amounts to demonstrating a certain isomorphism which relies upon the Riesz-Fischer theorem. Sophisticated viewers can go to Johnny von Neumann's "Mathematical Foundations of Quantum Mechanics" to get into the intellectual pathways. You have done a really good job demonstrating how basic wave equation theory available to an average undegraduate can make sense of the wave equation. Clearly a huge amount of high quality, thoughtful work went into this and it has not gone unnoticed.

I'm a high school senior deciding whether to go into medicine or physics, and this video helped me decide. Thank you so much!

I'm so happy you released a new video!!! Looking forward to diving into this later tonight!!!

Thanks a lot for doing this. Just two days ago I was thinking about googling Schrödinger's Equation to look for a video that explained it once and for all, and here you are. I remembered your voice 30 seconds into the video and got reminded that I already was subbed to your channel, and now I remember why. Probably the best presenter for physics videos on KZfaq in my opinion! Will try to support you somehow.

It is amazing how you develop and relate this beautiful equation (math-physical theory) in very simple way!! Thank you for your work!!

I have dwelled during the last 20 years into advanced electromagnetics struggled into Poisson's equations to solve boundary conditions using the Gradient operator, Maxwell's equations, potential vector, Gaussian probability function, Poisson's probability cumulative distribution functions, Swerling I and II and III, Markov's memory less probability to name a few...so I could understand every bit of your very successful work in producing such clarity, it even helped me put into perspective the importance of Louis de Broglie work on the dual nature of a wave, he definitely fulfilled the missing link between Einstein and Schrodinger and you have highlighted that so well. Respect to all the effort you have consumed in producing an excellent work.

I have rewatched the video and also written all your explanation myself by memory. I will watch it again sometime.

Absolutely marvelous. Reminded me of the days I learned this from Feynman himself when I was a freshman at Caltech. Many, many thanks.

Best physics videos I've ever seen, thank you for creating these videos.

This is the best and the simplest explanation I have ever listened to Very good job I indeed- thank you This lecture covered all of the basic and fundamental concepts in quantum physics, mathematics, and probability Thank you again

Complete explanation, you solve both simple problems and the difficult ones too which are given at the end of text books without solution! Thank you very much!!

Schrödinger also said: " I do not like it [the probability interpretation of quantum mechanics], and I am sorry I ever had anything to do with it. " Undergrads can relate.

This is a superb presentation. Extremely detailed. A lot to take in in an hour and a half maybe, but it would be a superb study tool alongside lecture notes.

I wish we had KZfaq back in the early 2000's when I was struggling to barely learn QM in college. You kids have it so good today.

This is an highly under rated channel… you can tell you really understand these concepts… I’m reading 6 numbers by Martin Reese right now it is nice to get some more detail on these subjects

Thank you so much for generating these explanations on this topic. Thank you for your hard work. It is one of the best explanation in the whole Internet. I like it very very much

Brilliantly and concisely explained! These videos have really helped my classmates and I out in our introductory quantum mechanics course. Hats off to you my man :))

Amazing. You can really learn anything on the internet these days. Thank you very much.

Taught in an excellent way! It’s a subject that can be difficult to grasp, and you’ve made it quite accessible while still including lots of detail. Thanks!

Sir, you are one of the best at explaining things. You made me see the underlying beauty of quantum mechanics. I understood each and every single bit of information you conveyed. I just love you keep working on such videos and keep enlightening the world.

Your meticulous attention to detail and clear exposition is marvellous. Thanks for these videos you provide.

The most excellent video I have seen on Schrödinger's Equation. Excited for your upcoming content.

I cannot thank you much for this refresher as I just planned on studying Quatum Mechanics again but in more detail this time

It's amazing that these Quantum Mechanic theories were created almost 100 years ago.