What is the Schrödinger Equation? A basic introduction to Quantum Mechanics

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 wave-function is used to calculate the expectation value of the position of a particle in a box. Stationary states are discussed, and it is 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.
References:
Quantum physics of atoms, molecules, solids, nuclei and particles - Eisberg and Resnick (Motivating the structure of the Schrodinger equation)
Introduction to Quantum Mechanics - Griffiths and Schroeter (Examples of expectation values and superposition of states).
Introduction to Quantum Mechanics - Phillips
Vibrations and Waves - King
The Quantum Story - Jim Baggot
Quantum Physics for Dummies - Steven Holzner
Thirty Years that Shook Physics - Gamow
Inward Bound - Abraham Pais
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You can follow me on Twitter: / physicsexplain1
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[@turtledruid464]

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!

[@PhysicsExplainedVideos]

Thanks for the kind words, much appreciated

[@masternobody1896]

@@PhysicsExplainedVideos brain left the chat

[@ionmurgu783]

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[@888waldi]

Jak długi jest bok sześcianu o objętości 31 ??

[@一个说话大声的中国人]

everything is a linear equation since Aristotle's freefall

[@galangal4803]

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

[@PhysicsExplainedVideos]

Thanks!

[@raymondfrye5017]

Taking a physics degree is not easy unless you really enjoy predicting the future. So how is the prophecy business today?

[@sethoflagos2880]

And congratulations too from one who graduated in Chem Eng a few decades ago. If you can reduce a class of partial differential equations to merely simplifying trigonometric expressions, then you've done your job as an educator. And done it well!

[@Imran52Feb]

@@sethoflagos2880 Yes, the way he attacked the problem by guessing the relation between k^2 and omega and then fitting the double differential wrt x and single differential wrt to t Schrodinger's equation using the standard wave equation is truly a smart methodology. Even the mysterious sqrt of (- 1) got explained . Hats off to him.

[@Imran52Feb]

Even the j got explained . I write j here since I'm an electrical engineer.

[@The578unit]

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.

[@PhysicsExplainedVideos]

Glad to help!

[@ss_avsmt]

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.

[@PhysicsExplainedVideos]

Glad you enjoyed it!

[@jacobsmith818]

Why the pride flag?

[@robandsharonseddon-smith5216]

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.

[@williamalldred2805]

Perfectly agree mate. Not something you can easily explain to the general public. Well done!

[@atomgutan8064]

​@@williamalldred2805 I honestly don't think that this video is watched by the general public or meant for the general public.

[@luckyizzac]

​@@atomgutan8064 well I haven't even reached college but I understood everything in this video This is a perfect video for a beginner

[@dutonic]

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.

[@germainguerin3063]

I would have written exactly the same thing ie it just surprised me that i could understand these derivations, same thing with the video on E=mc^2

[@chrisohagan8131]

I'm a biologist who was just about to give up on this because the math is a bit above my ability. But having read your comment I'm gonna stick with it a bit longer.

[@Am33304]

The mathematical and symbolic writing is fascinating but enigmatic to me. I can read it and read it without any boredom at all. But I don’t really have those maths. I think it all means something incredibly beautiful to me subconsciously. There doesn’t seem to be any other explanation for the experience, and in an odd way I seem to crave it. It’s like a whole world of concepts you could just dive into, but you had better be able to keep hold of the physical world around you. The urge even at my age to lose yourself in it sure is powerful, and there’s a caution I feel - to stay functional, to keep up with the responsibilities I have. I don’t know what it’s like for maths prodigies, but I think it must be dangerous and scary in addition to being magical. Wow, do I like this video!

[@CliffSedge-nu5fv]

To me, the math is easy on the mind, but hard on my wrist. Ow, damn hand cramps writing out every step..

[@kidus9311]

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

[@PhysicsExplainedVideos]

Cheers!

[@Casowsky]

If you've ever listened to the Numberphile podcast, this strikes exactly the same chord; the history adds so much to be inspired about to the story. And of course the beauty in the physics and maths. Incredibly engaging.

[@isobool3927]

Because Hitler read about the Schrödinger equation - he committed the Holocaust and the robbery and murder of over 27 million Russians.

[@Casowsky]

@@isobool3927 huh

[@isobool3927]

@@Casowsky Think about it: near to no Nazi got punished because nobody wanted to open that kid of reality to face the truth...because it doesn't only have to be that "the cat dies" by opening that lid - it can be so horrible that it "fries" the observer. We always focus on how the observation alters the observed...but it also alters the observer at the same time.

[@berryesseen]

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 KZbin 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.

[@IntiNikelaos]

As a physics major drop-out (I dropped out because of many things, some beyond my control, but one was that I had communication issues with most professors), I’ve never seen such beautiful and rigorous explanations for both such simple concepts and different areas of knowledge as what the standard deviation is and how the quantization of energy is related to the form of the wave function (that meaning, how the oscillating nature of trigonometric functions leads to discrete equidistant answers when solving trigonometric equations which leads to the energy states when solving the wave function. Literally, mind blowing!)

[@chuckstarwar7890]

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.

[@KonovDS]

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.

[@PhysicsExplainedVideos]

Thanks for the kind words and feedback, much appreciated!

[@amadalomusasia6317]

Only graduates of Physics can follow, let alone understand all these

[@pseudolullus]

@@amadalomusasia6317 Nope, many people who ain't physics graduates can understand

[@pseudolullus]

@pyropulse back when I studied chemical engineering we had to self-study the basics of the Schrödinger Eq. as our professor took it for granted.

[@urbankobal8154]

I think you have a good idea of what quantum mechanics is but I dont think you understand it completely, I think no one does lol.

[@jamesgalante993]

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 KZbin 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 KZbin--and I've watched an unhealthy amount of educational KZbin 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.

[@PhysicsExplainedVideos]

Cheers for the very kind feedback, it means a lot!

[@naayerhs7300]

Bro, I actually share your love for this guy. Na f that, I’m gonna flipping power that love to the 5000. Bruv, I’m with you, I thought water lewin was godly. Na, it’s this guy, I actually can’t believe even how well he explained everything from the beginning. I’m only 12 mins in, but I can tell it’s amazing. Thank you so much.

[@jeanlucas2834]

I KNOW EXACTLY HOW YOU FEEL

[@JG-zs8tr]

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. 👍🏼

[@PhysicsExplainedVideos]

Sorry to hear that you are in hospital, hope you feel better soon! Thank you very much for your support, it is very much appreciated :-)

[@michaeldamolsen]

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!

[@PhysicsExplainedVideos]

Glad you like them! Thanks for the kind words, much appreciated

[@ThatCrazyKid0007]

I cannot express how incredible this video is. Thank you so much for the work you do, I've never seen anyone on KZbin 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.

[@victorpeter222]

this vedio is good one

[@NoName-qv4zm]

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

[@PhysicsExplainedVideos]

Thanks!

[@justanotherguy469]

@@PhysicsExplainedVideos Heaven holds a beautiful place for those who try to help others.

[@Potencyfunction]

what bel is coming prize for who bcz I dont understand phisics and chemestry relation. I ussualy talk about CO2 but I dont understand how pleaseant or unpleaseant I am to talk with. I cant see the degree of one ´s intelligence in having a nobel .

[@JC-zw9vs]

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!

[@jeroenritmeester73]

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.

[@hughmungous1539]

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

[@PhysicsExplainedVideos]

Thanks, very much appreciated!

[@seanleith5312]

I am a science person, not a political person. But now I see the rainbow, it evokes the memory of disgusting flag flying in kids school. A beautiful image is ruined by those political hacks.

[@KalebPeters99]

@@seanleith5312 Totally unrelated and deeply unnecessary, Sean. Stick to being a science person...

[@seanleith5312]

@@KalebPeters99 I know, but can you blame me?

[@joshuaolian1245]

@@seanleith5312 are you shitting on gay people? or gay pride? like wtf are you saying?

[@millya6005]

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.

[@mdahdolan]

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

[@PhysicsExplainedVideos]

Thanks!

[@mdahdolan]

@John Casali Probably PBS Space Time and/or Dr. Becky

[@mdahdolan]

@John Casali I agree that he doesn't offer much mathematical derivation, but this approach isn't everything. Sometimes having abstract discussions or analogies help understand certain phenomena, and it isn't completely invaluable. Personally, sometimes I need someone to just point out phenomena and abstractly present them.

[@firstolasto1518]

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.

[@diribigal]

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.

[@PhysicsExplainedVideos]

Glad it helped!

[@dcrespin]

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

[@GoldInforcer]

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

[@m_bm_a7884]

The best explanation of Schrödinger Equation I have ever seen, now I know from where this equation did come from ...you have answered many questions I had before .. Thank you very much !

[@Bzl_777]

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

[@schmetterling4477]

Your mind will be blown by the insight, then, that the SE does not even preserve energy, momentum and angular momentum and that it can't explain chemistry, either. ;-)

[@johnjeffreys6440]

I think his equation is both right and wrong simultaneously

[@thanoskorovilas8899]

WOW. I am just left speachless at your work. This is truly a masterclass of teaching physics, the viewer never feels like something is missing from the explanation or something is arbitrary. Amazing work. I cant even imagine how long it took you to write the script for this video. Your channel is super underrated!

[@UjwalAroor]

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

[@PhysicsExplainedVideos]

Glad the videos have been helfpul!

[@justanotherguy469]

Its nice to see that there are people not involved in a university setting, that still enjoy and try to educate themselves on this most beautiful topic.

[@UjwalAroor]

@@justanotherguy469 yup a 100 percent! Im actually doing a degree in electronics engineering but i love quantum chemistry (and physics) way too much to also not learn it on the side.

[@justanotherguy469]

@@UjwalAroor Oh so that's your side piece. Nice!

[@seancheng3550]

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

[@wayneyadams]

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.

[@blythewarland6688]

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

[@EMWave]

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!

[@MyEyesAhh]

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

[@MLexploring]

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!

[@dice-uj2sr]

Were able to derive 2 integral 1/2cos(piex/a)-cos(3piex/a) from 2sin(piex/a)sin(2piex/a) I am stuck here 1:12:32

[@MLexploring]

I haven’t done this by my own. I just followed what he did. I also found a confusion in a previous integration in this video. But I skip as it is not my headech!

[@dice-uj2sr]

@@MLexploring oh sadge 😔

[@phart]

@@dice-uj2sr trig identity sinAsinB = 1/2 [cos(A-B) - cos(A+B)]

[@dice-uj2sr]

@@phart thank you so much really 🙏🙏🙏🙏🙏🙏🙏🙏👏 it just all clicked thanks a lot

[@douglasstrother6584]

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?"

[@attilauhljar3636]

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

[@PhysicsExplainedVideos]

Glad you like them!

[@cursed_dylan33]

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

[@PhysicsExplainedVideos]

Glad to hear it!

[@Kanjeeroboocho]

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 !

[@Potencyfunction]

I talk about past tense how do they found the correlation between those things ?

[@mayfield3314]

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 😁

[@roeljoseph7905]

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

[@PhysicsExplainedVideos]

Thanks!

[@schrodingerscat7218]

The word equimation is theoretical too.

[@peterwan9076]

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.

[@PhysicsExplainedVideos]

Glad you enjoyed it!

[@georgeaymes9211]

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

[@AndersWelander]

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.

[@garffieldiscool1163]

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

[@sekus]

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

[@PhysicsExplainedVideos]

Thanks you!

[@haydenwayne3710]

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.

[@tototriceps]

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

[@PhysicsExplainedVideos]

Glad you like them! Thanks for the kind words :-)

[@bogardchango.d.4598]

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

[@psy7251]

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!

[@PhysicsExplainedVideos]

Glad it was helpful!

[@solutions2exist556]

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.

[@steveklehfoth1503]

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.

[@Imran52Feb]

I too am an Electrical Engineer very much interested in Modern Physics. This video beautifully explains how our j appears in the wave function

[@pedrokahn5717]

By far one of the best materials concerning the basics of quantum mechanics on KZbin. 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!👏👏👏

[@heliogabrieldacunhabarroso5541]

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

[@Potencyfunction]

You shouldnt stop learning becauze something big will come. And when you are limitless than what can stop you ?

[@dominus_ignaviae]

There's no way my teacher finished such an eloquent concept in under 30 mins and went straight to problem solving. Thank you so much, teachers like you are a rarity these days❤

[@chaostheory567]

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

[@PhysicsExplainedVideos]

Cheers!

[@LiamDennehy]

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.

[@jonasdaverio9369]

You really should bridge that small gap you have in calculus. It won't take you that much time, and it really will help in your understanding of physics (and I think it will be much more gratifying)

[@EvillClown11]

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.

[@schmetterling4477]

Why are you learning engineering if your real passion is physics? You aren't making any sense. Just walk over to the physics department and learn physics. If you don't love engineering, then you will never be a good engineer.

[@EvillClown11]

@@schmetterling4477 Career prospects my friend. I cannot afford to base my degree solely on enjoyment given the cost of getting one. The graduate destinations of people with a physics degree did not appeal to me whereas the engineering ones did. I can always self educate as I have been doing, while still perusing my desired career path.

[@schmetterling4477]

@@EvillClown11 That's what every physicist wannabe thinks. In reality you are simply making fools of yourselves on the internet. :-) In any case... with regards to job prospects: I interviewed seven times in my life in total (that includes a student job and the interview for my PhD position) and I always got the job. Don't tell me that physicists can't get jobs, kid. You are completely clueless. ;-)

[@karlkarlsson9126]

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 KZbin in my opinion! Will try to support you somehow.

[@PhysicsExplainedVideos]

That is very kind of you to say, thank you!

[@go-away-5555]

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.

[@trumanhw]

Right, bc unless you understand what he's saying before he says it, you can't after. (how exactly would that constitute teaching ... verses summarizing? ) But FINALLY, someone who actually posts an honest comment. Everyone else here either already studied & was _SUPPOSED_ to understand it, or literally did before. Must've been a mystery to him why HIS teachers spent time explaining each idea when they need only assert it once? As [if] students need only hear assertions to have information transferred. Is this when he's supposed to say, "stop trying to hit me and hit me already." ??

[@go-away-5555]

I did it 😃

[@go-away-5555]

And yeah I planned on going hard on studying for 6 weeks and ended up taking 2 years don't judge me lol

[@jakkakasunset5485]

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

[@JohnDoe-wi6nq]

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 👌👌👌

[@edcoad4930]

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.

[@PhysicsExplainedVideos]

Thanks! Hoping to be able to post a bit more regularly

[@edcoad4930]

Couple of comments: I love the combination on both components of the schrodinger equation. I got taught independent version in year 2 and time dependent in year 3 which felt disjointed. Next point, continuing to love the "basic" maths of these videos which allows accessibility; Compton, Neutron stars, Black body all demonstrate the beauty of maths in physics (pet peeve of mine is mathematical rigour). Lastly, can we have a video on standard model and particularly particle prediction etc. The news last week talked about a 0.1% possible variation in the W boson...but why is it so exciting and why can't it be a new particle? Thanks again for these videos and the extraordinary effort to produce them.

[@TIO540S1]

You and Elliott ("Physics With Elliot") are gifts to those of us who yearn for explanations that are deeper than the usual Pop Sci. Thank you!

[@schmetterling4477]

What stopped you from reading a science textbook on the matter? Too hard? :-)

[@enriquemillanvalbuena5241]

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 :)

[@thegreatveil5699]

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.

[@PhysicsExplainedVideos]

Very nicely explained, thanks!

[@hgtrad7655]

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.

[@edwardarruda7215]

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

[@crt24501]

This might be the best video I've ever seen on KZbin, and I'm not restricting to the educational field.

[@mrpyfisher1995]

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!

[@PhysicsExplainedVideos]

Great to hear! Thanks for the kind words 🙂

[@craigfowler7098]

I studied this all over thirty years ago and forgot how beautiful the Maths was. This is an excellent video that brings it all back to me. Enjoy your course.

[@midaspool6229]

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!

[@fenrirwithatophat.26]

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

[@PhysicsExplainedVideos]

Thanks for the kind words!

[@ae-thermalconsulting1800]

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

[@tinastaley625]

My first time Kayaking and this Kayak held strong. kzbin.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!

[@goldengoat1737]

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

[@PhysicsExplainedVideos]

Thanks for the feedback and encouragement, really appreciate it

[@Potencyfunction]

The Martin is also in my perspective.

[@karkaroff1617]

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.

[@drbeanut]

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.

[@Imran52Feb]

This is the best video I have watched on Schrödinger's equation. I'm an electrical engineer by profession but modern physics fascinates me. The step by step heuristic approach by guessing a differential equation kind of relationship between k.squared and omega is just amazing. I always wondered as to how sqrt of minus 1 appears in the wave function and found the answer here. Thanks a lot, sir.

[@schmetterling4477]

Schroedinger is not modern physics. Schroedinger is the state of physics of 1926. It was obsolete in physics proper by 1928, when Dirac published the Dirac equation. You can't even do ordinary chemistry with Schroedinger alone.

[@Imran52Feb]

@@schmetterling4477 Could you suggest a video which lucidly explains Dirac's approach. Probably the makers of this video can throw some light on your comments about Schrodinger 's equation not being not Modern Physics ! I am not a Physicist but have found that Schrodinger's equation can explain some strange phenomena like quantum tunneling.

[@schmetterling4477]

@@Imran52Feb Not really. The reason why you won't find "real quantum mechanics" (by which I mean relativistic quantum field theory) on KZbin is very simple: it's tough sh*t. I mean, seriously tough. Mathematically you have to work a hundred times harder to understand the real theory than Schroedinger's toy model. That's why we teach non-relativistic QM to all of our physics students and maybe a few percent will go on and learn the real theory. Schroedinger doesn't explain quantum tunneling. It gives you an approximation, but doesn't tell you what is really going on. The reason for that is very simple: you have to stuff a classical potential in and there are no classical potentials in nature. There are only quantum fields. So all you are really doing with Schroedinger is to kid yourself.

[@Imran52Feb]

@@schmetterling4477 After your critical statement about the SE, I Google searched the difference between the two methodologies . Yes, the relativistic QM appears quite different and tough . I tried to understand the theory of tensors, but found it abstract and tough.Understanding the real beauty of Relativity requires a thorough knowledge of tensors. I have read somewhere that even Einstien had difficulty in getting full grasp on tensors and needed ( probably Le Cevita) to guide him. Could you please suggest how to Crack tensors?

[@Imran52Feb]

@@schmetterling4477 Further I think you are a professor of physics and have deep knowledge in this field. My regards.

[@peterhall6656]

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.

[@whatifschrodingersboxwasacofin]

What a wonderful comment! 👍

[@schmetterling4477]

Why are you telling us that you failed high school? ;-)

[@ZigSputnik]

@@schmetterling4477 What is the point of your stupidly negative and repetitive comments? Videos like this have been an fantastic revelation for many people who have found the subject difficult to grasp at school and from textbooks; or maybe have found the presentation of textbooks uninspiring. You obviously don't understand that people learn in different ways. Maybe you should read a textbook on it.

[@schmetterling4477]

@@ZigSputnik I had it with people who are throwing random scientific terms around without the slightest idea what they are talking about. Matrix mechanics and the Schroedinger equation are not equivalent. You can't get the proper continuous spectra with matrices. von Neumann's work is bare of any physics. He tells you the how but not the why. The dude even put the ridiculous notion forward that measurement has something to do with human consciousness. That's neither math nor physics. That's just total bullshit. Heisenberg and Bohr and Mott knew more about the physical processes years before von Neumann stripped the physics out. The wave equations don't explain quantum mechanics to you. You have to learn quantum field theory to understand what is really going on.

[@jonquil3015]

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!

[@jonquil3015]

Bug: sin is squared twice at kzbin.info/www/bejne/aIizcmSCbtp9p9E

[@wondererasl]

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

[@bkerdas]

Thanks a lot. This video will certainly find its place in the heart of undergraduate physics students in the world.

[@PhysicsExplainedVideos]

Glad it was helpful!

[@schmetterling4477]

And why would a smart undergrad come here to get a really poor presentation on the matter when he/she can find a hundred textbooks in the library that are much better? ;-)

[@shrirangsavale571]

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.

[@PhysicsExplainedVideos]

Happy to help!

[@Haldurson]

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.

[@phlynniii]

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

[@omerbar7518]

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

[@gmdchipzz8091]

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!

[@PhysicsExplainedVideos]

Glad you like them!

[@tochukwuezeaba1352]

I wish I can give you an award right now. You really demystified QM. May your life be as easy and beautiful as this video. I can't stop playing this video. Great work.

[@jezza10181]

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.

[@NumbToons]

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.

[@mrmadmaxalot]

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!

[@50PullUps]

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

[@williamworthy4091]

Incredible video. Never seen one video go from such basics to such profound conclusions. Can’t wait for the next one!

[@jamesbentonticer4706]

I've had my introduction to QM at university and I have to say, even though I had a good professor and good textbook, your explanation here is exquisite. Thank you for your time.

[@shonintobar979]

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

[@NoLuv4Hoz]

I don't know half of the math principles you employed, but I can easily recognize that this was quite a serious "basic introduction". It does inspire me to learn more, as there seems to be a whole major topic or lesson lurking at almost every logical step involved with deriving and explaining the all-important Schrodinger equation. Big thanks!

[@schmetterling4477]

One can't "derive" the Schroedinger equation any more than one can derive any other equation that is flat out wrong. At most you can start with something that would be far more correct, like the Dirac equation, and simplify it for the non-relativistic case.

[@necko2529]

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

[@mubasshir]

Wdym? I was here 2 days ago as well. The video didn't get uploaded?

[@BlazeOrangeDeer]

@@mubasshir it was, and it disappeared halfway through.

[@chrismuratore4451]

I think they decided to wait until World Quantum Day(April 14) to release it officially.

[@uvofsam]

He has to make some corrections so he pulled the video off.

[@skirby503]

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 :))

[@caltechharvard]

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

[@PhysicsExplainedVideos]

Glad you enjoyed it! Thanks for the kind words :-)

[@raymondfrye5017]

Harvard? Why not Stanford?

[@caltechharvard]

@@raymondfrye5017 Because those are the two schools I have degrees from. Post-doc was MIT.

[@raymondfrye5017]

@@caltechharvard Active in pure research? Most of my friends who went into physics ended up in Engineering to apply what they learned: Applied Physics. Regards

[@caltechharvard]

@@raymondfrye5017 Med School, then molecular biology. Wasn't smart enough for theoretical physics but did extremely well in MB. Research, pharma executive, then hedge fund. Now retired, dabbling in undergraduate reviews as in Feynman, Apostol, etc.

[@OSAMAMAful]

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!!