What is the Heisenberg Uncertainty Principle? A wave packet approach

In this video I would like to answer a simple question: according to quantum mechanics, how do you describe a freely moving particle? It sounds simple, but what we will discover is that by attempting to answer this question, we will actually uncover one of the most profound ideas in physics, Heisenberg’s Uncertainty Principle, which tells us that it is impossible to simultaneously know where a particle is located, and how fast it is moving, implying that there is a fundamental limit to our knowledge of the physical universe. It is a principle that lies at the heart of quantum mechanics, and it has revolutionised our understanding of the fundamental laws of physics. So, buckle up, and get ready for the ride.
References for this video:
Quantum physics of atoms, molecules, solids, nuclei and particles - Eisberg and Resnick
A student's guide to the Schrodinger equation - Daniel A. Fleisch
Introduction to Quantum Mechanics - Griffiths and Schroeter
Introduction to Quantum Mechanics - Phillips
Vibrations and Waves - King
Gabor Representations - Caltech (www.its.caltech.edu/~matilde/GaborLocalization.pdf)
Wave Packets and Dispersion - Matthew Schwartz (scholar.harvard.edu/files/schwartz/files/lecture11-wavepackets.pdf)
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: www.patreon.com/physicsexplained
You can follow me on instagram: physics_explained_ig
You can follow me on Twitter: PhysicsExplain1
iopscience.iop.org/article/10.1088/1361-6552/acdbb0/meta
iopscience.iop.org/article/10.1088/1361-6552/acfe54

[@PaulisInclusion]

Easily one of the best physics channels. Thank you for not dumbing things down and showing the math.

[@Patrick_Rangel]

Effectively, any attempt reduce the Physics the verbal expression, ignoring the Math, is condemned the futility chronic; *Physics without Math is stupidity!*

[@kenzzz3998]

This! ^ I hate when people try to make things too simple cuz I always feel like I'm missing a lot

[@richardleetbluesharmonicac7192]

The best scientists can explain complex concepts, anecdotally, and not have to show the math, which is not really relevant to the concept. Your air of superiority is kind of disturbing because it’s subjective.

[@fish1389]

@@richardleetbluesharmonicac7192 not really

[@andrewhancock2451]

Not only did he retain the details, but he presented them in very digestible form. You still need the tools (Fourier Transform, windowing, envelope modulation of a carrier, group and phase velocities, etc.), but if you have seen the concepts before, you have the high level view of how the come together.

[@spythere]

Wait, this video was already posted. But since nobody observed it it was at its superposition and now it was observed once more and become real.

[@xbzq]

I observed it but no one observed me so I'm like a cat in a box.

[@kallekula84]

He took it down while I was 15 minutes in to the video was super frustrating been waiting for the reupload since!!

[@p.b.2903]

I think he realized there were errors in his Euler equations. I think he just couldn’t help but take it down and fix it:

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@@xbzq Not a friend of Gene's, are you?

[@sachinsrb]

This is simply the best channel for real physics concepts rather than over simplifying things for a much broader audience for just awareness. Awesome work. Congratulations for a fantastic mathematical explanation. Using real mathematics is the key here. Thank you.

[@PhysicsExplainedVideos]

Wow, thanks! Glad you enjoyed it :-)

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No drama no time waste Pure knowledge a channel dedicated to the lovers of physics

[@NumbToons]

I was confused about how do we get localised wave packet by adding more and more waves. But HOOOOOLY, your video explained exactly that, and EXACTLY the same way I always try to understand things (by trying small experiments with equations, before understanding the final general result). Clearly the Best Physics channel.

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This is easyly the best channel that delivers lectures on physics.Your spot on explanations with respect to the choice of the applications of mathematics is really exemplary.Easyly the best teacher.Indelible comments.

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i was reminded of the phenomenon of beats in sound waves, where superposition of two similar frequencies creates a pulsing amplitude

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This has been my favourite channel for a while, I love pbs spacetime, veritasium, science click and watching lectures , but this is above

[@PhysicsExplainedVideos]

very kind of you to say

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Your ability to naturally bring your audience to understand fundamental laws of physics is unmatched as far as I'm concerned. Brilliant work again, thank you !

[@PhysicsExplainedVideos]

Thanks for the kind words, much appreciated!

[@NumbToons]

I was actually learning about Uncertainty Principle and everywhere I was finding same 5 lines over and over, I kept searching more and more. I kept video on hold for the end, so that when I have gained the general background for the topic, I will watch your video to finish it all. AND OH BOY! Did my plan work. This video cleared all my doubts and confusions about the uncertainty principle.

[@chandrasekarang948]

Never stop posting videos, you're the only channel that goes through mathematical details in depths. Thank you so much.

[@schmetterling4477]

Why do you want him to keep posting more bullshit like this? :-)

[@mosesgunn6937]

Your explanatory abilities are second to none. What a tour de force this is.

[@PhysicsExplainedVideos]

Glad you enjoyed it! Thanks for taking the time to leave a comment

[@school6268]

Best physics channel on the platform by orders of magnitude

[@PhysicsExplainedVideos]

Kind of you to say!

[@MagalaxeurDETER]

Bro are you a top physics teacher!? I haven't seen such clarity on how to explain the uncertainty pronciple in a short 1hr video. I had a full semester of quantum mechanics at university and not a teacher was able to explain the fundamental reason in 6 month time! Keep on making more videos please!

[@PhysicsExplainedVideos]

Glad that it has helped!

[@Shadowless_Kick]

With his in depth physics understanding and great math skills, he is qualified to be a top school professor than a “teacher”.

[@dartplayer170]

Definitely the best explanation of the Uncertainty Principle that I've ever seen

[@PhysicsExplainedVideos]

Glad it was helpful :-)

[@bathhatingcat8626]

What’s interesting is that it’s basic quantum- like 2nd year college stuff. He just explains it very clearly. Physics teachers can learn a lot from this channel

[@jamesbentonticer4706]

It's a shame you have to lose all those views that the original upload received. The clarity of your videos is fantastic and I appreciate the mathematical rigor you inclue.

[@cademosley4886]

I have a feeling those views came right back here as soon as they could. A person can't just watch it once. XD

[@jamesbentonticer4706]

@@cademosley4886 good point

[@Just.A.T-Rex]

It’s all good I sleep almost each night.😊

[@ToriKo_]

Why was the original removed?

[@escapeenrique]

❤i font earlier

[@momchi98]

Why in God's name was quantum never explained to me like this by my university. We did alot of exercises, but the principles like Schrodinger's equation and the uncertainty principle were treated like axioms. And it didn't take super advanced mathematics either. Thank you so much for this video. My passion for physics burns abit brighter every time I watch a new upload of yours.

[@PhysicsExplainedVideos]

Glad to hear it! Thanks for taking the time to leave such a positive and encouraging comment

[@cruser1381]

I admire your passion for physics. It’s so sad how these stories aren’t well told or known in popular culture. The transition from classical physics to QM is such a great story in human history and needs to be told better.

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I completely agree, an incredible story

[@Arthurnate]

Carlo Rovelli's Helgoland is a brilliant book on the discovery 🙏

[@peterfireflylund]

@@Arthurnate Three cheers for hay fever!

[@drbeanut]

This is awesome... I was recently playing around with the concept of HUP and was trying to figure it out myself. I took a different route. I just played with Desmos Graphs and manipulated sine/cosine wavefunctions until I got something... I arrived at the same result, and then worked backwords to find I was just adding together pure waves continuously. So much become so obvious in that moment. The single-slit, or what I really now think of as double-barrier, experiment REMOVES/DEAMPLIFIES component wavefunctions from the superposition, hence closing in on the pure wave, revealing diffraction gradients, instead of a "no-slit/no-barrier" laser dot.

[@mk-wo6jg]

This is the first video that made me want to sponsor a KZbin video. I just finished my undergraduate degree in astronomy and now I'm doing my master's degree in numerical simulation. Quantum mechanics is not essential to my research process, but I have always wanted to understand the principle of uncertainty. I also read shankar's book to myself, but I was frustrated because I didn't fully understand it. But this video gave me intuitive and perfect solution and confidence to read shankar's book again. Thank you very much. This short one hour video outperforms EVERY videos and EVERY QM lectures that I take in my undergraduate coures. Really really thankful to you.

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Either your country's educational system sucks lemons or you are lying about your education. Possibly both. ;-)

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Sadly, you're right.

[@schmetterling4477]

@@mk-wo6jg That was not much of a riddle.

[@mk-wo6jg]

Hahaha yes :( I think you are good at physics. Ur major also physics?

[@schmetterling4477]

@@mk-wo6jg PhD.

[@tjd_1274]

This is by far my favourite physics channel, it blends a mini-lecture series with a nice historical storyline. After doing a PhD the only chance you get to do lecture formats are at summer schools and you forget most of the undergrad physics which is way nicer to talk about with your friends. I look forward to your next video :)

[@peterhughes3648]

This is probably the best physics channel on the internet; clear, rigorous, and superbly well explained. Thank you.

[@chriszachtian]

Allready missed the Vid. Thanks for sharing knowledge with a certain background! Most other channels do not dare that. Hopefully, your success enforces you to continue.

[@PhysicsExplainedVideos]

Thanks for the kind words and encouragement, I really appreciate it!

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I can only imagine a probability distribution of the amount of effort you put into making this video. Thank you for your efforts, you have increased my understanding of QM, limited as our definition of understanding may be.

[@PhysicsExplainedVideos]

Glad you enjoyed it!

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Wow, this is really awesome. Makes me understand - or at least somewhat comprehend - wave functions in quantum physics nearly 20 years after I miserably failed at this in school.

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Huzzah! I really like this one because I feel like a free particle is the first most basic thing one should understand, and this explains it like a champ. The infinite square well is easier to get, but it feels more like a side road on the way to the real motorway. This is what I was waiting for.

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I completely agree, the free particle is a gem

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Another superb, detailed deep dive into physics. Top.

[@PhysicsExplainedVideos]

Glad you liked it!

[@petereldergill2942]

Been waiting months and am so glad you were able to re-post it. Hopefully be able to watch it soon. I need to make up and edit some physics exams first though. I love all your videos and thanks for such high quality work, mixing theory, history and general interest! Cheers from Toronto

[@PhysicsExplainedVideos]

Thanks for the comment and kind words, I really appreciate it

[@TheAngelOfDeath000]

Great video! I’m already in my first year of college pursuing my Ph.D in Astrophysics / theoretical physics, I specialize more in the study of black holes!

[@TheAngelOfDeath000]

In other news, where have you been man, it’s been 1 years? Are you ok?

[@multicoloredwiz]

Every time I watch a video you created, it's so succinct (I realize they're around one hour lol) and beautiful and satisfying.. thank you. I don't know how much time you spend on them, but you're a damn fine educator

[@PhysicsExplainedVideos]

Thanks for the kind words, I really appreciate it! Glad you enjoy the videos

[@jesse4202]

After months of struggling to understand this concept, coming back a year later with this video and being able to understand what seemed like such a complex topic is eye opening. Thank you again Mr. Explained for your work. Continue strong !

[@PhysicsExplainedVideos]

Great to hear!

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Brilliant video. I have understood more in 1hr than in my whole chemistry degree course more than 30 yrs ago.

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I am waiting anxiously for your new videos. Your ability to distill complex physics theories and math is so satisfying. By far, one of the best physics KZbin channels.

[@PhysicsExplainedVideos]

Thank you, very kind of you to say!

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A video in this style on gauge theory and forces would be incredible.

[@PhysicsExplainedVideos]

definitely on my to do list. Currently working on a video on the Dirac Equation. Working towards gauge theory

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a phenomenal supplement for reviewing for second semester quantum. Your channel is a godsend

[@PhysicsExplainedVideos]

Glad it was helpful!

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So happy to see a new video posted! These help me stay conceptually in touch with my university education that I don't get to use so much at work. Love sitting back and watching you explain the theory and the math!

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He's back! Very grateful for this content; high quality and accessible to everyone.

[@PhysicsExplainedVideos]

Glad you enjoyed it!

[@renedekker9806]

Absolutely love your videos. They are the physics videos that are the most clearly explained, while still going into all the details an math. It would be fantastically great if you could do a follow-up on this video, describing how things change for fast moving particles, taking Special Relativity into account.

[@anderoo9260]

Understanding this video and being able to calculate these things is my goal. I failed calculus in college a few years ago, so I'm starting at derivatives. I was always mediocre at best at math's and went downhill since high school. I absolutely detested math's But physics is so fascinating that I picked math up and been studying for a few months now. If I will be able to do this stuff, integers and all- I'll be a happy man

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Congratulations!! More than 10 million people have watched your terrific videos. You have an engaging teaching style and you do not scrimp on the Math! Its always a joy when you post a new one!!

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superb video, best physics channel on youtube. Period. Keep up the great work!

[@PhysicsExplainedVideos]

Thanks!

[@aditya.21]

Always love your work!! Never stop bringing to us more fascinating stories and concepts with fundamental Mathematical Approach!!

[@drbeanut]

Really connecting all the dots here. I think a great follow-up video to this would be how we go from the uncertainty principle in theory to how it reveals itself in experiment. Moreover, how particle-confinement changes the the time-dependent broadening, or how it is possible to produce the opposite result.

[@shazmunchdylbertoid]

I am so happy this is back up. thank you for your excellent work!

[@kevincleary627]

You are so great at explaing things at more than just a superficial level I would love to see you do a lecture on the Higgs mechanism in your usual level of rigor. Thanks for all your videos!

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Truly excellent, both in content and the pace of presentation. Love the visuals as they give an immediate intuitive feel for the equations. I totally agree that this is one of the best physics channels!

[@stauffap]

I've never seen this explained with such clarity. You resolved a question i had for a very long time and it was very easy to follow. I can't thank you enough!

[@lucyfrye6723]

Is this how it historically went down? We are looking for a wave that is localized, now lets find an equation that does this for us and the probability distribution just rolled out of it naturally because it was needed.

[@PhysicsExplainedVideos]

As far as I know, this is not the historical route to the uncertainty principle. Perhaps I will look at this in a future video

[@abrarjahin8848]

this channel is literally the best.. it helped me everytime i studied quantum physics

[@mdonnang]

For me the epiphany of this video starts at 50’55”: A brilliant visualization demonstrating the uncertainty of position and momentum relationship! I finally understood Heisenberg’s principle. Superb video, thank you!

[@PhysicsExplainedVideos]

Glad you enjoyed it!

[@alexfish8926]

this is such a perfectly timed video! i tried looking up heisenbergs uncertainty principle literally yesterday and couldnt really understand it!

[@PhysicsExplainedVideos]

Glad it was helpful!

[@iceman200200]

Wow, really excellent explanation. I've understood this information for a while (was a physics major), but never saw it explained so well

[@RD2564]

You do the math that I love only 10 times better than I can do it and that's what is great about this channel, thank-you for another wonderful lecture.

[@PhysicsExplainedVideos]

You're very welcome!

[@Jeducation22]

finally! I was about two-thirds of the way through the video before you took it down. The last week was like waiting for the next episode of 24!

[@PhysicsExplainedVideos]

Hope you enjoyed it!

[@prodTyeDye]

This is funny timing, I was just reading chapter 4, The Uncertainty Principal in Stephan’s Hawking’s “A Brief History Of Time”

[@PhysicsExplainedVideos]

Hope it helps!

[@Rudrakxh]

This is exact moment when Werner became Heisenberg.

[@hgtrad7655]

Top explanation, probably the best going through the maths. you even prepare the grounds for a knowledgeable reader to grasp the incredible implications beyond the narrative. Thank you.

[@highkey4316]

holy mother of god this was the perfect video. not all of the math was crystal clear to me as a first-year in college but the process you took in superposition made amazing sense. I can already see myself revisiting this video in future years as I continue in my quantum physics studies. thank you a million times over for creating this.

[@sphakamisozondi]

Bro, I thought you would never come back! Amazing content as usual!

[@ianmichael5768]

Although there will always be some uncertainty in my perception and understanding of reality (h), I truly thank you for creating this content and clarifying concepts. I used to hate superposition at university. Now, I walk in nature and enjoy the simplicity of it. Cheers

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This channel, and this Playlist specifically is helping me pass modern physics!!! Thank you for making this!

[@katm3428]

Execeptional video, exceptional analysis. I'm on my 3rd year of physics bachelor studies and, although I'm familiarised with these concepts for a long time, your analysis definitely cleared up a lot of ideas on the way for the transition from classical to quantum and your mathematical rigor is very much appreciated.

[@PhysicsExplainedVideos]

Glad it was helpful!

[@nemurerumaboroshi]

Fantastic stuff. Few pieces clicked into their proper place. Thank you!

[@PhysicsExplainedVideos]

Glad you enjoyed it!

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Man, I miss your videos, please upload more!

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That was mesmerising , thank you so much for taking the time to prepare such a beautiful presentation. 🙏

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Excellent work... as usual !!! Coincidentally, I was teaching the exact same concept in the exact same way to my engineering students a few days back. This will be a great resource for them. Thank you for this.

[@PhysicsExplainedVideos]

Great 👍

[@anthonycbash]

With no training in physics nor complex mathematics, and only a certain degree of understanding about the idea of Heisenberg’s Uncertainty Principle, I was nonetheless able to follow your lecture to the end and gain what feels like a more substantial grasp on what is perhaps going on in the real world when a particle, like a photon, a proton, a neutrino,etc, is traveling through spacetime, and why it is so difficult to actually determine where it is or how fast it is moving with any certainty. The math is very important in attempting to describe what seems to be happening but I could not help but think that there may be the possibility that some of the uncertainty might be a result of how the equations are set up in the first place. On the other hand, attempting to explain how a particle can behave like a wave and vice versa seems to be a tremendously difficult task, to say the least.

[@PhysicsExplainedVideos]

Glad it was helpful! Thanks for taking the time to provide feedback, much appreciated.

[@ezequielwolcan7632]

Excellent video! I watched it twice and when I went for the third I saw it had disappeared. I am very grateful it's back!

[@Hkj2000]

As it so happens, I was studying the same topic on my own and this video really helped me clear the fussiness in the concept I had in my mind. Thank you so much for creating this amazing video. I spent a lot of time and effort trying to understand this topic better.

[@PhysicsExplainedVideos]

Glad it helped!

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This is a phenomenal video! I wish it had been around when I was studying physics in the late 90's! You do a great job of simplifying the arguments, while still staying strong on scientific roots!

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This is a very good piece of work. Well done!

[@eamonnsiocain6454]

Excellent! Thank you!

[@PhysicsExplainedVideos]

Glad you enjoyed it!

[@steveboigon5478]

Good Day! its been a year since you have posted a new Video. I love your work. You are a great teacher and the videos are very inciteful and very well done. Please let me know if you are planning on posting more content or if you have abandoned Physics Explained. I am sure others are also wondering about this. Personally, i hope that you will continue.

[@andycremeans]

I just watch these over and over until it sinks in 😂❤

[@PhysicsExplainedVideos]

:-)

[@EMWave]

I am big fan of your channel. Again one more wonderful insight into world around us. This is a beautiful explanation of Uncertainty principle

[@PhysicsExplainedVideos]

Many thanks!

[@danoneill8751]

I like the way you include all the maths but breeze through it so that we can see results dotted through the hour. To think I used to score in the top 5 at uni every exam, but 20 years later its like hauntingly familiar gobbledegook. Really like the content level judgement though Mr. Physics Explained. It's like neat 'half way house' (half way on a VERY logarithmic scale) between a normal TV documentary where they show the odd result and literally no context so that the result really means nothing and is misinterpreted by absolutely everyone, and a physics lecture in the middle of a degree, where they you might spend 3 2-hour lectures diverting to JUST the calculus around Gausians with an anticipated 6 hours of personal study to accompany them, and that's assuming you are already coasting through the calculus classes accompanying the rest of the degree at that point and didn't get drunk once in the last 2 weeks, otherwise multiply the 6 by three to catch up, and then 2 weeks later get to the satisfying result (by which time you've forgotten everything about k-space anyway and need to recap for at least 6 hours, and the meanwhile Andy seems to be able to do the cryptic crossword during lectures and still do the weekly assessed questions in just a few hours, oh and despite being that level of clever he has a girlfriend unlike literally anyone else on the course. Damn Andy. Lost his job apparently after the brexit vote caused BAE systems to fire about a 5th of their best graduates so was forced to move to the US, messages me occasionally about how 'the fall' in Masetusettes is so much nicer than Bristol... git.

[@PhysicsExplainedVideos]

This is one of my favourite comments of all time, made me laugh out loud. Thanks!

[@steveboigon5478]

Several have commented that since you have not posted in more than a year, and have not responded to questions about your videos, that we can only assume that you are no longer active here and have moved on.. I will no longer check in here looking for more content. I really enjoyed the videos you did post, and I wish you well. If I am incorrect, and you will continue posting, then please let your followers know

[@drbeanut]

Last part of the video was beautiful mathematics, well done sir.

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love this channel to show us beautiful structure of math under the physical concept!

[@jameselliott216]

Easy to make me happy. The graphics coincide with the commentary.🤩Haleluejah!

[@PhysicsExplainedVideos]

I’m particularly glad you like the synchronisation as this is the part of the video production that takes the longest

[@jameselliott216]

@@PhysicsExplainedVideos it is greatly appreciated. keep up the good work!💯

[@albertwesker9119]

I've waited a lot for your video and it's finally here

[@PhysicsExplainedVideos]

Enjoy!

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I love this video. Such a satisfaction to connect the dots in my patchwork of knowledge about this stuff.

[@PhysicsExplainedVideos]

Glad you enjoyed it!

[@nahichak1003]

FANTASTIC VIDEO. GREAT JOB. THANKS !

[@vermasean]

So glad I stopped by the channel; my alerts were set, but didn’t get the notification. Love the work! 🙌

[@PhysicsExplainedVideos]

Thanks!

[@eeshtarr]

Kudos for pronouncing "de Broglie" correctly. You are one of the few.

[@PhysicsExplainedVideos]

It has taken me years to get this right!

[@theonlinezone6904]

thanks for explaining where formulas comes from, it makes a lot easier to understand this complex topics

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It is a joy to congratulate you for a second time on this video.

[@PhysicsExplainedVideos]

I appreciate it twice as much ;-)

[@cenk_tuna]

I managed to follow up to the end with 40 mg of Ritalin but I got a really good intuition. Thank you.

[@liamkamphuis3300]

Nothing short of another absolutely fantastic Physics Explained video. Love your great work, excited to see whats next!

[@watermelon9209]

super informative! Expecting your next video!! many thanks!

[@PhysicsExplainedVideos]

Glad you liked it!

[@mctrafik]

Took me 3 sessions, but sat through the whole thing. Nice. Love this content.

[@PhysicsExplainedVideos]

Glad you enjoyed it!

[@julius-theodorbarth3893]

Man your videos are a blessed miracle, just fantastic

[@PhysicsExplainedVideos]

Thanks!!

[@stewarthayne8304]

Thanks for producing these with the math!

[@Sol-En]

Briliant explanation !

[@PhysicsExplainedVideos]

Thanks!

[@Sol-En]

@@PhysicsExplainedVideos Tell me please what application do you use for animations ? I also want to do something like this

[@NEWDAWNrealizingself]

THANKS ! MATHEMATICALLY AND ELEGANTLY EXPLAINED THE UNCERTAINTY RELATIONSHIP, WELL !

[@tupublicoful]

Best class I ever saw on the uncertainty principle. Others dumb down much of the derivation and flail miserably with hand wavy explanations on what the wave is doing.

[@schmetterling4477]

If you want the actual derivation for general linear operators, then you should look at a textbook about functional analysis. To the mathematicians this is a trivial lemma. It has absolutely nothing to do with physics. ;-)

[@mariocesarsousa]

Very carefully and beutifully explained❤❤❤❤ Need to watch again taking notes.

[@drbeanut]

Would be nice to have a side-video to this where you demonstrate why a general shape envelope is bounded by the gaussian envelope.

[@angeldude101]

The uncertainty principle is really just a normal phenomenon with all waves, quantum or otherwise. The tricky part is relating momentum to frequency. Once you do that, the concept of position doesn't even make sense. What is the "position" of a wave when it's just a pure frequency? The only way to actually get a position is to collapse it down to the point that it's basically a particle again, but particles generally don't have frequency, so if momentum is frequency, then a pure particle simply doesn't have a defined momentum. It was interesting going through the math to prove this though, and how the exact constants come about.

[@schmetterling4477]

It doesn't even require waves. Mathematically it's a trivial lemma about linear operators.

[@makespace8483]

Just superb!

[@PhysicsExplainedVideos]

Many thanks!

[@petereldergill2942]

Unfortunately I didn't get to quantum for my students, ran out of time and the pace of our course was a bit slow. A I'm couple of my students have watched a few of your videos but it is a bit advanced for the majority of them. They quite like them but have difficulty getting through the whole thing without getting lost. I think the length is fantastic and I try to watch multiple times to understand as best I can (I've never studied quantum). There's a joke I hear one time: Me: "I can't find my keys" Physicist: "You must have know too much about the momentum" Furthermore, keep them coming Cheers from Toronto

[@PhysicsExplainedVideos]

Thanks for the feedback, much appreciated! It is great to hear that you and your students are watching these videos. Reassure your students that it is often the case in physics that we don't understand everything (I still struggle with many topics) but that you can gain interesting insights even if you can only follow 20% of the mathematics

[@theunknown4834]

Just curious, why was this reuploaded?