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
You can help support this channel via the Physics Explained Patreon account: / physicsexplained
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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

[@ozzymandius666]

@@PhysicsExplainedVideos Pure physics gold. Your pedagogical technique is without peer. I love physics, but I'm so so tired of the people that shy away from the math. This man is providing a public service that very few truly appreciate. The man actually shows you how it works. Perhaps he'll do a solution of the Hydrogen atom, ortho- and para-, and maybe a bit about helium, with a 1S and 2S occupied by electrons of the same spin. Perhaps this man will do something else, perhaps about the Higgs mechanism and the Standard Model, but I know whatever it is, I'm gonna like it. Hip Hip Hooray for Physics Explained and the man behind it!

[@ozzymandius666]

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[@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!

[@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.

[@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.

[@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!

[@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.

[@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?

[@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!

[@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.

[@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

[@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.

[@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 :-)

[@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!

[@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

[@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.

[@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.

[@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.

[@mdahdolan]

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

[@PhysicsExplainedVideos]

Thanks!

[@mdahdolan]

@@johncasali4559 Probably PBS Space Time and/or Dr. Becky

[@mdahdolan]

@@johncasali4559 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.

[@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 .

[@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!

[@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

[@khangungtung8636]

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

[@seancheng3550]

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

[@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

[@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!

[@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!👏👏👏

[@masterparticular]

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

[@bzl7956]

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

[@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.

[@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!!

[@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!

[@shonintobar979]

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

[@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.

[@tariq5783]

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

[@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!

[@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!

[@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.

[@roblouw1344]

Thanks for a brilliant video! The effort you put into it is phenomenal. Very well presented! As a senior citizen, I have understood every bit of it. Well done.

[@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!

[@sekus]

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

[@PhysicsExplainedVideos]

Thanks you!

[@arjunsinha4015]

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

[@bogardchango.d.4598]

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

[@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.

[@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!

[@52n1]

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

[@atomjack]

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

[@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 👌👌👌

[@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 ?

[@joyboricua3721]

This presentation is a jewel in KZbin's discissing academic content, IMHO. Excelent work! Certainly looking forward to seeing the next one.

[@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 :)

[@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

[@user-er4no9op3u]

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 ?

[@farzanroshdieh698]

The way all these are explained in this video is astounding. What an achievement.

[@cosmicnomad8575]

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

[@PhysicsExplainedVideos]

Glad you enjoyed it!

[@garffieldiscool1163]

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

[@feandil666]

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.

[@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 :))

[@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

[@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!

[@chaostheory567]

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

[@PhysicsExplainedVideos]

Cheers!

[@magicofscience8899]

Very easily explained. I am really thankful to you from bottom of my heart. I think that you have kept the concept above your personality. Mostly highly learned persons are not able to explain well because they impose their personality to the explanation.

[@nycsimon2024]

Just want to say thank you for making this course. You make me understand my one semester QM introductory course much much better 😊

[@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?"

[@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.

[@jasonsutton4415]

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”!

[@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!

[@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

[@MohammadYoussof]

It's the finest explanation of the Schodinger equation I've ever heard. Thank you very much!

[@SixTimesNine]

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 :)

[@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 😁

[@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.

[@JumpingCow]

Wow! This was about a half of my introductory QM course in 1 1/2 hours. It is so clear, and so amazing that a) the universe works this way and b) people discovered these equations!

[@umami0247]

I'm not going to even speculate on this. I'm just glad there our people out in this world that can do this and understand it. You do a great job of presenting this as you do with all the video's I've seen from you.

[@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!

[@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

[@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.

[@annapreidl5843]

what an unbelievably clear explanation. summed up three weeks of QM class in 1.5 hrs

[@fenrirwithatophat.26]

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

[@PhysicsExplainedVideos]

Thanks for the kind words!

[@taherjijel518]

Many thanks to you for these highly well structured and fluente videos on the matter. I hope that you will be rewarded a way or another. I always loved physics and your amazing way of presenting it gives the desire to go back to studies even am over 50. Again; thanks a lot.

[@thevaliantkautilya]

Thanks a lot for bringing such videos in Physics which remains my first love to this day. Have subscribed with the hope you keep publishing such videos going forward as well

[@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.

[@Martin666Taylor]

Really pleased to see this video is back. Many thanks Physics Explained

[@PhysicsExplainedVideos]

Thanks!

[@LuisBrandoIngTec]

I've just seen the first twenty minutes and simply can shout "outstanding!". A very awkward matter explained so simply... Excellent 👏👏👏

[@swampwiz]

This is a wonderful presentation that shows the path from the Planck's postulates (necessary to explain the ultraviolet catastrophe) to Schrödinger's resultant equations.

[@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.

[@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 :-)

[@Ihab.A]

I subscribed to you channel, and frankly speaking, I first click on THUMBS UP, then watch the videos because I know the quality of the information in your videos will always surprise me and be very interesting. Thanks

[@Kathedore]

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

[@jaimelonify]

Incredible work! Thanks a million for your time, effort and talent.

[@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.

[@user-uv7ug1du4n]

The most beautifully explained Quantum Mechanics ever !!! I can't take my eyes off the screen for the whole presentation. What an amazing refreshment ! Thank you so much.

[@subhadey8593]

I've learned the finest thing of science, throughout by this video, appreciated myself mostly, thanks you're really a mind blowing professor.. Love you dear. Sir you need more and more this type of content, very interested as science undergraduate student.

[@vijaybelapurkar814]

This is the best explanation ever of a complex subject like Schroddinger Equation. I until now avoided trying to understand it but not with your video explanation. I wish you bring out videos on Relativity and Sting theory.

[@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." ??

[@borisbukalov9407]

Great explanation! My students and I really enjoyed it!

[@cenkkurt5582]

You have covered the subject in a very broad and detailed manner. I thank you.

[@EmanueleFrasca00]

Beautiful video, the level of detail is really outstanding! Thank you

[@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. ;-)