Schrodinger equation

Physics Explained 120K subscribers This video provides a basic introduction to the Schrödinger equation by exploring how it can be used to perform simple quantum mechanical calculations. After explaining the basic structure of the equation, the infinite square well potential is used as a case study. The separation of variables approach is used to solve the Schrödinger equation and Born's probabilistic interpretation of the wavefunction is used to calculate the expectation value of the position of a particle in a box. Stationary states are discussed, and it is then shown that a linear superposition of energy eigenstates leads to non-stationary states with uncertain energy. The oscillation frequency of a simple superposition of states is calculated and comparisons with radiation emission from atoms is discussed. You can help support this channel via the Physics Explained Patreon account: https://www.patreon.com/physicsexplained You can follow me on instagram: https://www.instagram.com/physicsexpl ... You can follow me on Twitter: https://twitter.com/PhysicsExplain1 624 Comments rongmaw lin Add a comment... TurtleDruid TurtleDruid 3 weeks ago 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! 298 Physics Explained Wayne Adams Wayne Adams 2 weeks ago 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. 4 Kidus 93 Kidus 93 3 weeks ago I love how you start building up from the historical background, something we don’t see often. I hope you will upload more often❤️ 69 Physics Explained Denis Konov Denis Konov 3 weeks ago 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. 76 Physics Explained Attila Uhljar Attila Uhljar 12 days ago Just the perfect amount of details. The depth and breadth of these videos are fantastic, thank you for putting all this effort into them! 4 Physics Explained Rob And Sharon Seddon-Smith Rob And Sharon Seddon-Smith 3 weeks ago 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. 59 Physics Explained Galangal Galangal 3 weeks ago Having taken a physics degree many decades ago may I congratulate you on such an excellent presentation. 46 Physics Explained tlxyxl tlxyxl 3 weeks ago (edited) Great explanation, as someone who just got bachelor degree from a STEM area of study. I found the explanation surprisingly easy to follow, as the reasoning are built on top of calculus, linear algebra, and probability theory, all of which I am somewhat familiar with. The only small thing I haven't heard mentioning is in 1:05:07, that expression looks quite similar to the Fourier series of a periodic function. And if that's case, the coefficient Cn is the Fourier coefficient, which represents the magnitude of a sinusoidal wave of a particular frequency. The subsequent analysis regarding orthonormal property also reminded me the orthogonality of Fourier basis, which looks exactly the same. Are there some connections here? Can we interpret those coefficient in that way? 2 Physics Explained Oyibe Chibundu Oyibe Chibundu 3 weeks ago (edited) 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? 43 Physics Explained Sebastian Jastrzebski Sebastian Jastrzebski 3 weeks ago Massively excited for the new content. Everyone of your videos is a treat for the mind. Cheers! 37 Physics Explained Ujwal 9000 Ujwal 9000 3 weeks ago 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 16 Physics Explained Laurens Veraart Laurens Veraart 3 weeks ago 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 😁 6 Senh Mo Chuang Senh Mo Chuang 3 weeks ago Beautifully explained! What a great refresher of QM with valuable illustrations 9 Physics Explained MrPyfisher199 MrPyfisher199 3 weeks ago 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! 28 Physics Explained Arnav Salkade Arnav Salkade 3 weeks ago (edited) fantastic. truly helpful. I wish uni professors could teach as well as this. 16 Physics Explained John Alberts John Alberts 3 weeks ago Brilliant explanation.There is so much content squeezed into this single lecture. 15 Physics Explained Student McStudentface Student McStudentface 2 weeks ago 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 3 karl karlsson karl karlsson 3 weeks ago (edited) 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 Youtube in my opinion! Will try to support you somehow. 2 Physics Explained Wyrmhero 42 Wyrmhero 42 3 weeks ago This is one of the best Youtube videos I've ever seen, Period. Thank you so much for posting these great videos. They habe inspired me greatly in pursuing a course of studies in physics and becoming a physicist to expand mankind's knowledge of our universe. Keep up your amazing work <3 Greetings from Germany :) 5 Edward Arruda Edward Arruda 3 weeks ago Excellent. I wish this was available 30 years ago when I took physical chemistry. 11 Physics Explained S B S B 3 weeks ago 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! 18 Physics Explained J C J C 3 weeks ago 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! 10 Physics Explained Chuck Starwar Chuck Starwar 3 weeks ago 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. 2 Fenrir! With a top hat. Fenrir! With a top hat. 3 weeks ago Best physics videos I've ever seen, thank you for creating these videos. 9 Physics Explained P S Yee P S Yee 10 days ago 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! 2 Physics Explained Michael Dam Olsen Michael Dam Olsen 2 weeks ago 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! 2 Physics Explained MRShockwave MRShockwave 4 days ago (edited) I cannot express how incredible this video is. Thank you so much for the work you do, I've never seen anyone on YouTube 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. 1 Physics Explained Jeroen Ritmeester Jeroen Ritmeester 3 weeks ago 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. 11 Physics Explained No Name No Name 3 weeks ago Man, you should be given a Nobel prize for putting this all together. Very good explanation! 11 Physics Explained Jim Lunde Jim Lunde 3 weeks ago I appreciate the work you put into this video. Thank you and great job. I'm just a guy interested in physics and this excellent video helps me gain an appreciation of what quantum mechanics is and where these concepts come from. Bravo. 2 Physics Explained Waltz Ng Waltz Ng 2 weeks ago (edited) Great job. I never thought I could understand quantum mechanics to this level. Now I understand why it's so difficult to reconcile general relativity (GR) and quantum mechanics (QM). GR looks at spacetime and QM looks at space and time. The basis of these two theories differs in fundamental way that I think without some breakthrough in our understanding of spacetime (space/time) it is impossible to reconcile GR and QM. 1 KOSM0S KOSM0S 2 weeks ago 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. 3 Physics Explained Hayden Wayne Hayden Wayne 2 weeks ago 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. 2 Physics Explained Helio Gabriel da Cunha Barroso Helio Gabriel da Cunha Barroso 3 weeks ago (edited) That is the clearest introductory video about this subject I've ever seen. 👏👏 I'm very excited for the next video 6 Physics Explained diribigal diribigal 3 weeks ago 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. 10 Physics Explained Peter Wan Peter Wan 6 days ago 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. 1 Physics Explained Blythe Warland Blythe Warland 3 weeks ago for a lay person that is interested in science and physics, this is a great explanation of something I have struggled with for years 13 Physics Explained RCY RCY 2 weeks ago 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 Youtube 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. 3 Physics Explained J G J G 3 weeks ago 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. 👍🏼 10 Physics Explained Shaken, Not Stired Shaken, Not Stired 2 weeks ago This is such a great video. Now, I have a much better understanding of the basics of QM. Thanks a million 2 Physics Explained Shrirang Savale Shrirang Savale 3 weeks ago 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. 2 Physics Explained Daniel Crespin Daniel Crespin 8 hours ago (edited) 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 https://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 Douglas Strother Douglas Strother 3 weeks ago "Quantum Mechanics: Foundations and Applications" by Arno Bohm This is a graduate-level text (or advanced undergrad text), so don't start here; however, the writing style is very clear and crisp. The author approaches Quantum Theory as an algebraic structure built to explain measured phenomena, like Werner Heisenberg. It treats states as vectors and observables as operators on those vectors. 1 TotoTriceps TotoTriceps 3 weeks ago These videos are PERFECT, not so thourough as a college course, but detailed enough to get a real understanding of the concepts. Great job keep it up :D 1 Physics Explained Regal Regal 3 weeks ago As a chemist, this video has really put more context and polished up my knowledge and appreciation for quantum mechanics. Even if I'm not a physicist, I really enjoy your videos and it lets me appreciate that science more. 4 Physics Explained forgor forgor 3 weeks ago Amazing job you did on this video. Keep it up! 3 Physics Explained Steve Klehfoth Steve Klehfoth 3 weeks ago 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. 1 Jason Jack Jason Jack 3 weeks ago Excellent video! I have been looking for something like this for ages. I decided a while back to learn, to the best of my ability, GR and QM. While there are several good videos available for GR I have found nothing good enough on QM - until now! Thank you so much! Looking forward to the next one :) Bharat Gopalakrishna Bharat Gopalakrishna 3 weeks ago 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). 7 Physics Explained Will Hopkins Will Hopkins 3 weeks ago Hey this is just an excellent video. I particularly liked the history and motivation that led Schrodinger to his equation. You mention in the video though that he had some more esoteric reasoning behind his original derivation. Can you shed some light (no pun intended) on this? 1 Douglas Strother Douglas Strother 3 weeks ago 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?" 2 Physics Explained Richard Freeberg Richard Freeberg 2 weeks ago Great introduction to the math behind the mysterious quantum mechanics. My early math education was subpar but now in my seventh decade I find great satisfaction in discovering what I missed many years ago. Your delivery is excellent although a bit fast for my old brain. Never the less,, I really enjoyed the whole journey even though I didn't understand half of it! 1 Physics Explained feandil666 feandil666 3 weeks ago Thanks, a lot of concepts of quantum mechanics that I had just accepted, now make total sense as a natural consequence of the analysis of this equation. 2 Karkaroff Karkaroff 3 weeks ago 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. 3 Gsjxbx BXhdhs Gsjxbx BXhdhs 3 weeks ago Just found your channel. This is inspirational, and it makes me want to continue studying Math and Physics even more! 2 Physics Explained Princeofcups Poc Princeofcups Poc 11 days ago (edited) What's always fascinated me about Q.M. is that in classical physics you study a phenomena and derive the underlying math, but in Q.M. you take the math and then look for evidence to confirm it. 1 Physics Explained Rajarshi Sen Rajarshi Sen 3 weeks ago It will be very helpful if you often bring videos on different topics of physics. Your content quality is very interesting 4 Physics Explained randy martin randy martin 3 weeks ago Wow 90 minutes rightly spent on this guy:) Thanks for coming back! I have watched your Einstein special relativity over and over it's so good. Looking forward to General Relativity and Dirac equation , ha but we might need to learn semi Riemannian differential geometry and Tensor calculus first though eeek. 2 Physics Explained Dr.Beanut Dr.Beanut 3 weeks ago Thinking in terms of probability, perhaps Born’s rule can be made sense as follows: there are actually 2 wave functions describing the particle, Psi and Psi* which are complex conjugates. Each actually describes a probability, but it is the two probabilities multiplied together which describe the probability of observing the particle. Perhaps they are individually probabilities of where the particle is from different perspectives of time (forward/reverse), and the true probability is the probability of those together. Just as with any other probability, you multiply probabilities of two events to get the probability of both events. 2 hugh mungous hugh mungous 3 weeks ago Watching your content is like watching a new lemmino video for me; an absolute treat! 72 Physics Explained Moh'd-Eslam Dahdolan Moh'd-Eslam Dahdolan 3 weeks ago One of the best Physics YouTube channels, probably top 2 or 3 in my opinion. 18 Physics Explained BikeArea Tirol BikeArea Tirol 9 days ago 5:01 - 5:31 This is the key to Schrödinger's motivation to finally find his personal meaning of life. : ) 1 cursed_ dylan cursed_ dylan 3 weeks ago cant believe you came back with this absolute 90 minute banger. your work always inspires me to keep studying and it keeps me motivated 4 Physics Explained Alex Miller Alex Miller 3 weeks ago This brought so much insight into something that at first seems so counterintuitive, but upon investigation, makes sense once it is derived. I wish you well in your studies and career my friend! 1 Physics Explained Oh God Not This! Oh God Not This! 3 weeks ago Magnificent video. Really well done. 3 Physics Explained Arjun Sinha Arjun Sinha 3 weeks ago The most excellent video I have seen on Schrödinger's Equation. Excited for your upcoming content. 2 Physics Explained The Great Veil The Great Veil 3 weeks ago (edited) 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. 7 Physics Explained memyself memyself 2 weeks ago Wow, Mr. Physics Explained, you gave us a complete course in Quantum Mechanics in a nutshell without shying away from any detailed step. Every necessary mathematical step is there! You even stuck in a short course on Probability Theory, because it was a necessary detail that you weren't afraid to tackle and include. My only question is, how many sittings did it take you to make this video? It's so seamless, it seems that you did it in only one sitting, but I doubt that was the case, was it? 3 Physics Explained Ing. Luis Brando Ing. Luis Brando 13 days ago I've just seen the first twenty minutes and simply can shout "outstanding!". A very awkward matter explained so simply... Excellent 👏👏👏 Liam Dennehy Liam Dennehy 3 weeks ago 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. 6 Physics Explained ray herman ray herman 3 weeks ago Every wave requires the energy to oscillate between two parts, typically the potential energy like the tension on a string, and the kinetic energy like the motion of the string. This is modeled as the real and imaginary parts of the complex number representing the wave solution. Both parts are necessary to understand the wave. When the motion of the string goes to zero the tension of the sting is necessary to complete the cycle. Alex Goslar Alex Goslar 3 weeks ago Thank you for a great, simolified explanation. saad aijaz saad aijaz 3 weeks ago I cannot thank you much for this refresher as I just planned on studying Quatum Mechanics again but in more detail this time 5 Physics Explained GMD Chipzz GMD Chipzz 3 weeks ago 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! 5 Physics Explained حسام الدين حسام الدين 3 weeks ago Thank you very much for the hard work you do you are one of the best education channels and you can see that by your hard work 1 Physics Explained Jorge Malosti Jorge Malosti 3 weeks ago man, when you found the square root of negative one, my brain just exploded, such a beautiful result i'm high of physics at this moment 3 Physics Explained Hugo Hugo 2 weeks ago Ive always found it ludicrously amazing how abstract math has parallels to the real worls Johnny Toobad Johnny Toobad 3 weeks ago I took a "Modern Physics" course in college..way back when. I love the history behind how these dudes "discovered" all this stuff. 1 Physics Explained Mann Mann 3 weeks ago brilliant, keep up the good work mate! 2 Physics Explained Bernard Deham Bernard Deham 2 weeks ago Thanks a lot for this outstanding video ! I'll need to watch it more than once, keeping a pencil next to me to take notes. I'm about 70 and my calculus and maths skills are far behind. Thank you also for your very clear English pronouncing, indeed, my mother tongue is French... 1 Physics Explained Sam W Sam W 3 weeks ago Excellent and beautifully done. Always look forward to your wonderfully crafted videos. Physics Explained Hardik Parekh Hardik Parekh 2 weeks ago Excellent introduction..👏👏👏👏👏👏👏👏 What's most interesting part of video for me is the physical reasoning of deriving the SWE and why it is different than standard wave equation. Potential in a well is classic example to demonstrate the power of SWE in explaining some real life scenarios. Requesting you to add one more lecture on application of SWE for hydrogen atom for 3 spatial dimensions to show how 3 fundamental quantum numbers arise, how it correctly predicts Bohr orbits an Bohr energy (some part of this is touched in this video as well), how SWE is solved for particles whose wave functions interact with each other (which leads to Pauli's exclusion principle) and solving SWE in light of special relativity to show existence of spin and anti-particles(Work of Paul Dirac).. I know I asked a lot but understanding these issues with physical reasoning rather than only mathematical treatments makes things more relatable.. And I am sure you can deliver such physical reasoning for these topics the way you have dealt with in this video.. For now, looking forward for your next video on quantum tunneling.. 50PullUps 50PullUps 2 weeks ago I wish we had YouTube back in the early 2000's when I was struggling to barely learn QM in college. You kids have it so good today. 1 Jimmy Zhao Jimmy Zhao 3 weeks ago It's amazing that these Quantum Mechanic theories were created almost 100 years ago. 4 N G N G 3 weeks ago (edited) 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. 2 Michael Michael 3 weeks ago It would be interesting to see a video done how Newton developed calculus 3 Physics Explained Sergio Lucas Sergio Lucas 2 weeks ago Amazing video in all the aspects, thank you :) Alexander Juda Alexander Juda 3 weeks ago Learning about QM is difficult for me because the material is chopped and scattered all around. A single 1h30 video is a brilliant way to let the viewer connect the dots. Thank you. 1 Physics Explained Jason Sutton Jason Sutton 2 weeks ago This is a wonderfully rigorous explanation for the rather puzzling principles in quantum mechanics. I must admit when I was hanging onto your mathematical proofs I dreaded the word “next”! 1 George Aymes George Aymes 3 weeks ago 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 Iliyan Popov Iliyan Popov 2 weeks ago Your work is truly amazing sir. We all admire you very much. 2 Ishan Agarwal Ishan Agarwal 3 weeks ago Thank you very much for explaining this complex topic so beautifully and intuitively 2 Physics Explained atomjack atomjack 3 weeks ago I'm so happy you released a new video!!! Looking forward to diving into this later tonight!!! 2 Physics Explained Joe Wanyoike Joe Wanyoike 3 weeks ago Excellent, I actually understood this 👆🏾 2 Physics Explained Axelius Axelius 2 weeks ago Fantastic work as always! 2 Physics Explained Hai-Duy Nguyen Hai-Duy Nguyen 3 weeks ago (edited) The man, the myth, the legend. He's back 😎. Would you consider doing a video about Leptons? I was thinking along the lines of Steven Wienberg's paper 'A Model of Leptons' and how this is at the heart of the Standard Model 3 Physics Explained lee wang lee wang 3 weeks ago I always loved this stuff. PS 42:30 "And, therefore we can write the following green yellow expression for the probability..." I'm guessing Schrodinger had a good set of coloured pens when he was doing this. PHYSICS HALT PHYSICS HALT 3 weeks ago The best channel to provide real and quality content..... really meaningful content bro ... please upload more and more like think...link plz on string theory 6 Physics Explained angeldude101 angeldude101 3 weeks ago (edited) When cos wasn't enough to act as the quantum wave function, my reaction was to say that the classical wave function was incomplete. Why? Because it only included half of the circle! By half, I mean variously the even half, the symmetric half, or the x component. You're still missing the odd half, the antisymmetric half, or the y component. That's what sin is. sin and cos are the two halves of the exponential function, but not quite. The exponential function as is when split in half gives hyperbolic sin and cos (sinh and cosh). sin and cos are only what happens when you fold the exponential in on itself rather than having it escape to infinity. To do that, you need to work in a bounded space: spherical geometry. i is the number that brings the exponential out of the hyperbolic world and into the spherical world. Every time I see a cos or sin, I assume that the other has to be hiding nearby, and that they're not separate, but two halves of the whole. Even in the classical string wave, only one of the parts forms the physical movement, but the other is probably hiding in the system somewhere, likely in the energy or tension or something. Martin Taylor Martin Taylor 3 weeks ago A lovely video that will bear repeated viewing. Looking forward to the follow-up video on quantum tunnelling 3 Physics Explained Kerry White Kerry White 13 days ago What a superb presentation, which sometimes requires a full semester to learn. 1 Physics Explained James Galante James Galante 3 weeks ago 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 YouTube 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 YouTube--and I've watched an unhealthy amount of educational YouTube 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. 1 Physics Explained David Nash David Nash 3 weeks ago Thanks, I didn't understand the full history or where the complex term appeared from, very enlightening. Najah Naffah Najah Naffah 3 weeks ago Excellent lesson ! Thank you 1 Abhinav Abhinav 3 weeks ago Sir, in real sense, your channel is gift from God in this 21st century. Love it whatever you do 😇😇 1 Physics Explained Arthur Ogawa Arthur Ogawa 5 days ago I enjoyed following your discussion! Especially your "derivation" of the Schrödinger equation. Physics Explained Jon Quil Jon Quil 3 weeks ago Wow! When I did physics decades in the past, no one (NO ONE) in the class understood the mumbling about the Schrödinger Equation. There was more value in just the first half hour of this video than in the several hour-long lectures inflicted on us! 1 Ruhail Ruhail 3 weeks ago (edited) This is so brilliant I have no words. I always hated quantum mechanics because it was introduced to me in such a terrible and nonintuitive way. We were introduced to idiotic dirac notation first which seemed so weird and made up that I was completely turned off by QM. We were introduced to Schrodinger equation later in the course but by that time I just didn't want to learn the subject and unfortunately failed. Thank you for reviving my interest in QM 2 Physics Explained Ian Michael Ian Michael 3 weeks ago Yes. There certainly is a lot of uncertainty in predicting the future. Excellent content! 8 Physics Explained Piyush Chauhan Piyush Chauhan 2 days ago Great work. Thank you ❤️ 1 Physics Explained Martin Taylor Martin Taylor 3 weeks ago Really pleased to see this video is back. Many thanks Physics Explained 4 Physics Explained caltechharvard caltechharvard 2 weeks ago Absolutely marvelous. Reminded me of the days I learned this from Feynman himself when I was a freshman at Caltech. Many, many thanks. 1 Physics Explained Haldurson Haldurson 3 weeks ago 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. 2 Physics Explained Khalid Al.harbi Khalid Al.harbi 3 weeks ago I hope this vedio was uploaded before my modern physics exam. Great work, very clean and clear explanation. it is acctuly scary how you explained what took our doctor a month in just one and haft hours. keep it up and I look forward to your next video. 6 Physics Explained David Sykes David Sykes 3 weeks ago Excellent work. I almost understand it,need to watch a few more times. 1 Physics Explained Premdeep Khatri Premdeep Khatri 2 weeks ago What a wonderful video is explaining Schrodinger Equation. Thank You so much for this video. 1 Stella Stella 3 weeks ago you have the best content, interesting long simplified physics videos 2 Physics Explained yahia walid yahia walid 2 weeks ago This is an absolute masterpiece 1 Blue Raja Blue Raja 3 weeks ago (edited) 54:47 "Likewise, the expectation value can be written as [integral over Ψ* x Ψ dx]" This needs more explanation. Shouldn't it be [integral over x |Ψ|²dx]? I assume they're the same (|Ψ|² = Ψ* Ψ, and complex multiplication is commutative), but that leads to a new question: why would we want to write it in that more complicated form? Jake K. Jake K. 2 weeks ago Fascinating video, even though I couldn't understand a thing of it. Great work on these! 2 Physics Explained Yuriy Krivosheyev Yuriy Krivosheyev 3 weeks ago