Quantization and Heisenberg's Uncertainty Principle

[@chriscross1152]

Hi Sir, i teach Physics in Belgium. I've watched many of your lectures about Electomagnetic radiations, classical mechanics, waves and so on. There's one thing i'd like telling you : you're one of the greatest pedagogue i've ever seen and heared. Thanks for all.

[@lecturesbywalterlewin.they9259]

Thanks, Chris, for your kind words.

[@sanjayj7456]

Do they need Physics teachers in Belguim?in your University?I like to explore and teach as much as possible as in India there is no much scope or respect in Science

[@enochbrown8178]

Absolutely!!!

[@tenzin9327]

As a student I think he is one if the best teachers even among his fellow MIT professors.

[@p.tswaraj4692]

good sir

[@lemont2005]

Dear Mr. Lewin,I´m a medical doctor from Brazil who loves and studies physics ( every single day ) and your lectures ( all of them ) made me feel that I'm on the right way. World would be a very very different place to live if it was full of men like you...Thanks for everything....we love you!

[@lecturesbywalterlewin.they9259]

Thank you for your kind words. I have two friends .in Brazil. They both study Physics. One of them finishes her studies now here in the US.

[@ranjitprasad2155]

I also love physics.

[@Baraa.K.Mohammad]

Oh my god! I'm also a medical doctor.. well, not yet (I'm in my last undergraduate semester).. but I've been in love with Physics and Cosmology since I was a kid... I've been reading and watching lectures and videos about both topics since I was in junior high school. I actually think about getting on the right path, pursuing my true passion, studying Physics and Cosmology on a more professional level. Anyways, I love to see that there's a medical expert that has interest in Physics, because I think you already know that this is a really rare thing, lol. Cheers from Syria!

[@lintunoo1394]

Also Medical doctor from Myanmar, South-east asia country, who love Physics since high school. My tuition teacher Aung Mya Oo, also demonstrated some experiments his best in small scale. Love to see your Lecture Prof.Lewin. Hope I can meet & buy your books.

[@harshmaurya7143]

I' am pretty sure that even his camera man's will be good in physics

[@Amansarkar700]

Yes indeed

[@dharmikmistry8781]

😂

[@AjayKumaryoutube786]

😂

[@mialmastaposeia]

Dear Mr Lewin, I am so touched by your lectures that you make even feel emotional. Thank you very much

[@lecturesbywalterlewin.they9259]

Thank you

[@alexluthorkos5252]

"The more the universe seems comprehensible, the more it also seems pointless". Steven Weinberg

[@lecturesbywalterlewin.they9259]

:)

[@nicksokolov6024]

just a small reminder since we are reminded of Newton being English ; Niels Henrik David Bohr (Danish; 7 October 1885 - 18 November 1962) was a Danish physicist together with Werner Karl Heisenberg; 5 December 1901 - 1 February 1976) was a German theoretical physicist, The Copenhagen interpretation was first posed by physicist Niels Bohr in 1920. Albert Einstein was a German-born theoretical physicist and so on.

[@342MrIncredible]

i did masters in chemistry .... though i like physics .... and every aspiring teacher should learn how to teach from him .... great respect

[@MrXeberdee]

Fantastic! I was uncertain about Heisenbergs principle, but Mr. Lewin shed light on it. Brilliant lectures, so clear and informative.

[@sameerkhnl1]

Sir the influence your lectures are having on those who are deeply curious about the world is beyond words. Your lectures, and the fact that you have made them available on youtube is a legacy and will have served to make a dent in the universe. Huge respect sir!

[@lecturesbywalterlewin.they9259]

Thanks Sameer for your kind words

[@tomwapin2693]

Dear Mr. Walter I'm from Vanuatu..I really love your lectures it makes me feel interested in physics ...your illustrations about the equations were really relevant ..

[@boyanfg]

Sir, it is the passion about the subject and about teaching it that makes your lessons shine. It is an inspiration. Thank you for sharing this with a broad audience.

[@Dr10Jeeps]

As a university psychology professor myself for 45 years, I can only stand in awe of Dr. Lewin. He is simply amazing and I thank him from the bottom of my heart for enriching my hobby of studying physics.

[@thegonz1447]

i understood about 15% of that, but thoroughly enjoyed all of it.

[@beautifuleducation3172]

sir i am an undergraduate student from pakistan.i think physics becomes so cute if taught by great teachers like you.Thanks A lot for providing us enjoyable , thinkable readable and above all lovely physics.

[@BatDan513]

At work and at home, I have two flat-screen monitors that are arranged side-by-side. Now, there is typically a very small gap between the two bezels of the monitor screens where they meet in the middle. Occasionally, I would notice something strange in this small aperture between the monitors: the color pattern or visible texture of the wall behind the screens would appear to be "magnified" in the tiny gap as compared to above the screens. I often wondered what this strange apparent lensing effect was caused by - maybe some "penumbra effect", I wagered. But then I watched your lecture. Now I know what I am seeing is HUP in action!! This fascinates me to no end: That this strange "lensing" of the light reflecting off the wall through the gap in my screens is no optical illusion, but a fundamental property of nature as given by HUP!

[@lecturesbywalterlewin.they9259]

can't help you

[@BatDan513]

@@lecturesbywalterlewin.they9259 Not a help request - just stating that your lecture helped me to understand why something appears to be distorted as it is viewed through a small gap, from some distance away. It is quite fascinating.

[@anantdesai2751]

I have been a fan of Feynman since high school but his lectures couldn’t come close to explaining what Professor Lewin does here. Simple and bulletproof!! Watching this version added another nugget of knowledge that just by confining an electron to a hydrogen atom, it moves at very high speeds and has energy.

[@lecturesbywalterlewin.they9259]

thanks for your kind words

[@dr.marwanalam]

its was extremely interesting way to teach the uncertainty principle, i find it lovely, normally you have to focus on some thing but this, what i found is developing your focus, you dont need to force your self. thank you professor

[@DavidTJames-yq9dr]

you are amazing. I cannot believe that I comprehend this. Thanks a million to your lecture. You are a rock star superhero!

[@lecturesbywalterlewin.they9259]

:)

[@harshavardhanasrinivasan3125]

Tremendous work sir ,now currently i am pursuing my undergratuate .I am a great fan of your teaching .I have been watching your lectures since my high school days .Great works and you stand as a perfect example as how a teacher should be !

[@viraj_mehta]

This lecture of yours can be put in the top 5, if not the first position. Just FANTASTIC, both, the knowledge & the way you presented it.

[@lecturesbywalterlewin.they9259]

thank u 😊

[@walidnouh1747]

Lecture that illustrates eloquently the beauty of science as a poetic language that enhances the beauty of nature around us .. god bless

[@lecturesbywalterlewin.they9259]

:)

[@20bluebug]

Thank-you good sir for making these lectures available this way! I'm really loving these!!!!!

[@theoneclutchgod2885]

Sir, just to give an example of how good you teach, I'm in standard 9th and i can understand all of these topics without a doubt. Absolutely love you teaching style ❤️ Huge respect

[@lecturesbywalterlewin.they9259]

Keep watching

[@rebokfleetfoot]

i realize not how lucky i was to be a student, half asleep while a brilliant man explains amazing things about nature :)

[@SirRandallDoesStuff]

I am getting my PhD in Physics and I still love to watch your videos. I really enjoy a well put together lecture.

[@lecturesbywalterlewin.they9259]

Thank you for your kind words

[@sanjayj7456]

MSC specialisation? Solid state?PhD topic? semiconductor? or Thin Films?

[@Logan753-g1v]

I wish I had Walter Lewis as a teacher. My current teacher just reads off bullet points from a PowerPoint and prints off practice questions from the internet.

[@aljim2889]

ur not alone

[@lecturesbywalterlewin.they9259]

Logan, Many teachers in the world work exclusively with powerpoint. They eve show derivations in power point. It's very very very sad. Students only benefit from lectures if the teacher derives the derivations on the black board. Power point is basically "showing" the students what's in their books. No need to go to lectures. very poor teaching!

[@arkadiptaghosh99]

i agree.....student needs to see the equation building up.....that's why you are the best in the business...

[@sanjayj7456]

If you are a student and you require classes I can teach you online. Via Skype. I'm a Physics lecturer and I have my coaching classes. Regards,

[@sanjayj7456]

Sir Lewin, is a great Physicist and MIT Professor, I love the way he teaches and demonstrates.I agree with you as many teachers, just use power point via laptop and never do any derivations or equations or numerical. I do teaching Physics and I always solve or derive every relations to prove how the concept and knowledge has been used in Physics and how they are inter related I have worked at NIO, Goa India for 7 years as Research Scientist.I always use marker pen and keep solving equations just the way you do using chalkRegards

[@mdshoyebshah8713]

What a great way to explain the Uncertainty Principle practically.. Truly you are one of the greatest physics teacher

[@mitochondria7321]

when i was in high school ,i use to say what a damn subject is physics ,one of the lecturers of mine in pre university told about u sir, then i started to view ur lecturing on physics, today i am able to answer every thing practically ,and iam inspiring many other people about physics ,thank u very much ,a love from india and india need lecturer like u sir.

[@ashitbarank]

You are lovable in India too . I wish , I wish even at this age to go back to pre university level to have a professor like you . God bless America for having a genius like you .

[@shubhamsrivastava4403]

I'm feeling satisfaction when after finishing 8 years of my student life I understand this topic (and many more) Thank You Sir

[@gobngrg883]

You are one of the greatest professor I've ever seen to my life. Your lectures has motivated me alot to perceive the physics in the different way from that of a common person. I feel so lucky about myself to be a part of your lecture series. Thank you very much for being so down to earth, professor Walter Lewin. Love from Nepal ❤️❤️

[@lecturesbywalterlewin.they9259]

Wow, thank you!

[@kddk8584]

A lifetime of learning in a one hour video. Thank you for making and sharing this video, it's fantastic.

[@nicksokolov6024]

Born Ernest Rutherford 30 August 1871 Brightwater, Colony of New Zealand, could not go directly to Oxford or Oxford as it was reserved for English born. He was among the first of the 'aliens' (those without a Cambridge degree) allowed to do research at the university. It was an interesting story how many hops he had to make and be well known to be an alien at reserved universities of UK. He is not English he is Kiwi, his parents were immigrants from UK.

[@andrewsparkinson1566]

Mr Lewin your work is inspirational. Thank you for sharing your love for understanding.

[@pong336]

You just explained one of the most challenging topics of physics in such an easy way, you’re definitely the Feynman of the 21st century.

[@THEDHL184]

I Love You Sir. We are unprivileged for not getting a teachers/professors like you. As you know our country INDIA. Where student sucide for KNOWLEDGE. Please speak about Something on Indian Education System so that international educated community concerned about that. Thank You

[@deepaktripathi4417]

I've always wanted to study Physics but by the time of my highschool I didn't have much knowledge about it and didn't have any mentor who could guide me what exactly Physics was.After my Highschool I had to chose commerce and that was due to lack of money and guidance. But now when I have a smartphone I can watch Pro. Walter Lewin's lectures on KZbin. I really enjoy your lectures sir! We love you.🙏

[@lecturesbywalterlewin.they9259]

That's awesome!

[@manishmane2231]

Thank you, Sir for your lectures. They are very helpful.

[@lecturesbywalterlewin.they9259]

:)

[@KrishnaCalling]

Legs touch from India...Gurudev..you are such an inspiration to all teachers of world

[@shubhankardasgupta4777]

JEE Aspirant here, Gearing up for the JEE MAINS 2021. Learning this all under the age of 18 just puts me to flex a bit on people with that ages. LOL, have fun :)

[@arifbaloch238]

Sir I am watching all your lectures. Love and respect from Pakistan.

[@patrickario5259]

Hi professor I am a physics teacher in Uganda I love your lecture and I do pray to one day reach in your lecture room physically.

[@familytriate]

Today, I learned what quantic phisics is about, great explanation, example that excellence is acheve when you do what you love

[@shubhamkalravevo1884]

Thnx sir....you are a great teacher.... lots of love from india

[@Schrodinger.cat3]

This was the best explanations i ever heard of uncertainty principle.

[@jpphoton]

Tremendous lecture from a truly talented gem of a man.

[@ChemicalMan]

Hello Sir, I'm from India, It's really awesome, I also become like you.

[@nambrvan]

Professor Lewin, greetings from Serbia. You are wizard! Why I didn't have physics teacher like you are? :(. Physics isn't math, physics is nature. Physics isn't for physicists, its for all people! Thank you a lot! This is magic!

[@TanPale]

Thanks for being so concise, it really helps me focus and follow along.

[@lecturesbywalterlewin.they9259]

:)

[@mianakhtar2089]

this is the best lecture on Heisenberg's uncertainty principle.

[@lecturesbywalterlewin.they9259]

:)

[@USER-jo7yz]

I sent this lecture to my grandson who studies physics in Groningen continuing the tradition.

[@lecturesbywalterlewin.they9259]

prima

[@USER-jo7yz]

@@lecturesbywalterlewin.they9259 Thank you and be healthy sir!

[@adampinkerton8659]

Thanks Dr. Lewin on the positron thing; I spend 99% of my time on M-Theory.

[@lecturesbywalterlewin.they9259]

excellent!

[@kaustavbhattacharjee224]

Your teaching is the right way for physics teaching

[@lecturesbywalterlewin.they9259]

:)

[@meow75714]

This is the finest explaination of Heisenberg's Uncertainity principle. I am really curious to find out how did Heisenberg actually derived this formulation? Can you please give us pointers to reading material in this regard or best thing would be if you can derive the equation for us. Much respect.

[@solconcordia4315]

If we assume that a planar wave exp(i 2π/lambda times x) multiplied by an unknowable unit-norm phase-factor (which produces the uncertainty in the measurement) is an eigenfunction, we can derive the momentum operator from de Broglie's relation.

[@Devatheertha...]

Dear mr lewin i am from Kerala your class.... I really love your lecture 🥰

[@mursaleenshafi1933]

I love him....he makes these beautiful concepts come alive

[@mudithawanniarachchi4838]

You are a hero to the world sir!

[@baskarbalsu8863]

Extraordinary teacher ! Thank you Sir!

[@arthurmee]

Walter Lewin . . .what a wonderful teacher and a lovely man.

[@somendrapal9271]

Being a physics teacher I enjoy your lectures immensely

[@lecturesbywalterlewin.they9259]

great!

[@ultimate01]

❤️physics and ❤️ you sir Sorry but ❤️ physics> sir But you are one of the greatest teachers in the world and you made me love physics this much ...

[@lecturesbywalterlewin.they9259]

:)

[@jimwinchester339]

This was a really top-notch presentation.

[@khaliqurrahman3703]

Dear Professor, Thanks for the lovely demo of the uncertainty principle. I can do it at home, though not that neat. However using a minute pin hole, the spread of the circular smear seems much less. Is it because, now the problem is no longer one dimensional? How about the calculation? May you live forever. Best regards.

[@lecturesbywalterlewin.they9259]

I can make the opening of my slit 5 microns. You cannot make your pinhole 5 microns. Thus your spread will be much much less. But even if you could make it 5 microns too little light would go through. I always use the slit because the amount of light that goes through a slit t 5 microns is about ten thousand times more than what goes through a pinhole of 5 microns. My laser beams are about 4 mm wide. Thus I win a factor 4*10^(-3)/5*10^(-6). A pinhole is the wrong way to go. Show less

[@khaliqurrahman3703]

Thanks for the explanation. My slit experiment (a cut with a fine knife on a piece of paper and shining a laser) gives reasonable result. Best Regards

[@lecturesbywalterlewin.they9259]

:)

[@khaliqurrahman3703]

Sorry to bother you again. The expression for angle θ (Lecture 34, Fall 1999) after substitution of variables, depends only on the ratio of wavelength and slit opening (Planck constant cancels out). Is it not little strange that the final calculation is independent of the value of the Planck constant? One could do the experiment with longer wavelength (won't be visible and hence less exciting!) and increased slit opening, right? Best regards

[@lecturesbywalterlewin.they9259]

It's not strange that h does not enter into my results. I have treated here light as waves. Once you do that, you "bypass" Planck. Photons (EM radiation in general) are bizarre. To say that they are waves is incomplete, to say that they are particles is also incomplete. To say that they are both is also incomplete. The rules for EM radiation are fundamentally different from our Newtonian way of thinking. ANY picture that we paint in our heads is wrong. Its behavior is crazy but it's the way the world ticks"

[@khaliqurrahman3703]

Yes, I see you bring in deBroglie and I suspect that now we have wave viewpoint for the LHS and particle viewpoint for the RHS of the equation. Thank you so much for your kindness answering my questions. Best regards

[@zahidurrahaman428]

Thank you professor. You are really amazing. You made me to think that actually how to think?

[@tashi2009]

You are 10000 times better than my school teachers. . .

[@dmitry926]

The Planck constant defines spin of elemental particles which is the same as vibrational rate in metaphysics that allows to make objects invisible ("move to another dimension").

[@manishk45]

As usual this was a terrific lecture about the intricacies of quantum world. I have a few doubts. Is it really a good idea to draw parallel between quantization of energy level of electron and quantization of height to which a tennis ball will jump? The other thing that I wanted to ask is what if we keep on decreasing the size of the triangle so that the ball has no place to move. seems like if we bring particle at rest it will have define position as well as defined momentum, i.e. zero. Also will you tell me about momentum of light photon?

[@lecturesbywalterlewin.they9259]

p=E/c

[@lepidoptera9337]

The "particle in a box" system doesn't have a well defined momentum. The system is not momentum conserving and "the particle" is not in a momentum eigenstate.

[@biiianciii888]

27:40 THANK YOU! I speak a little bit of dutch and had an ongoing dispute with my classmates over the correct pronunciation of Huygens, now I will send them this video to show I was actually correct ^^

[@gerardomoscatelli8584]

Google/KZbin : please do a favor to humankind and de-rank all the pop mystic pseudo explanations of quantum physics on KZbin and put this Master Class as the Mandatory Number 1 - Must See - Absolutely Necessary video to really start understanding quantum physics . Thank you Dr. Lewin for your infinite valuable contribution to human knowledge.

[@deepveshraj7984]

thank you so much walter lewin ,,,love from Nepal , Kathmandu

[@harishnadhareddy1480]

Guru ( my head keeps on your feet ) 1) Can it assume as diffraction because when light is passing through narrow slit this can bend through two edges of slit ? 2)can we predict the changing of momentum of laser light keeping a screen on it. (Like zinc sulphate of rutherford experiment).in that case light can be able to see like billarad ball in triangle.

[@ajcook7777]

I thought Max Planck introduced the idea of quantization?!

[@lecturesbywalterlewin.they9259]

Yes he did in his blackbody equation.

[@timbeaton5045]

@@lecturesbywalterlewin.they9259 As basically a mathematical "trick" to explain why the Rayleigh-Jeans predictions suffered from the "ultraviolet catastrophe". In an analysis of black body radiation, he realised that there would be an infinite number of energy levels (standing waves, in effect) and that they should all have an equal share of energy (this is a huge simplification!). This meant that the higher frequencies would dominate the energy spectrum which was simply not what was observed. He introduced the idea of quantisation to "limit" the number of allowed frequencies, and it suddenly produced what was recognised as the characteristic spectrum of Black Body Radiation. The next problem was to ascertain what that quantity would look like, in terms of value. Experiments then led to the discovery of the size of what is now called Planck's Constant. I seem to have read that Planck himself was somewhat skeptical, at least initially, that this was anything but a quirk of mathematics, but it soon became part of the bedrock of QM.

[@sumanghosh6704]

@@timbeaton5045 wow❤️❤️❤️❤️

[@sanjaypaswan5693]

@@lecturesbywalterlewin.they9259 Yes sir Discontinuly Discrete packets of energy called Quanta

[@tomneedham1937]

OMG! This is THE FINEST lecture on QM I have ever listened to or viewed. Prof Lewin is Zeus! Having tried to get my head around QM for many years - and failed miserably - this lecture has blown away much of the fog that obscured it for me. As a student in the "University of KZbin", why has it taken so long for me to find your lecture(s)? Keep up the good work Walt - as Bob Newhart would have called you. Maybe you can explain why the Uncertainty Principle did not prevent the use of tobacco when introduced to Europe by Sir Walter Raleigh! Question: would you be able to explain in conceptual terms why QM & GR breaks down at the singularity that existed at the moment of the Big Bang? Many thanks for a GREAT lecture!

[@lecturesbywalterlewin.they9259]

>>> Question: would you be able to explain in conceptual terms why QM & GR breaks down at the singularity that existed at the moment of the Big Bang? Many thanks for a GREAT lecture!>>> There is not yet a theory on quantum gravity. String theory my be our best bet (in the future).

[@madeincda]

Don't tell me you're another string theorist?! Haha regardless, this being my first time watching your lectures I am already subscribed. Thank you for translating physics to laymans!

[@JK-ru7sj]

Such a amaizing teacher 💗

[@aljim2889]

Seriously Dr. Lewin, I might change my major. I am loving this stuff.

[@lecturesbywalterlewin.they9259]

:)

[@ankitroy5868]

Indeed, It give me Sleepless nights thinking about this!😃

[@socotroquito2007]

Yep the spectrum colors , quantum leap is like violin or guitar music were notes are singular and do not grow by keeping the finger attached , each state is singular and do not overlap or gets each wave a distinct note ,never as shades of color

[@surendrakverma555]

Excellent lecture Sir. Thanks and Regards 🙏🙏🙏🙏🙏🙏🙏🙏

[@lecturesbywalterlewin.they9259]

Most welcome

[@glutinousmaximus]

Wonderful stuff Walter - a nice refresher!

[@lecturesbywalterlewin.they9259]

:)

[@terencewinters2154]

Now you can study physics from MIT without going to MIT.

[@kimjong-un4521]

Finally understood it. Thank you, sir.

[@solconcordia4315]

The Uncertainty Principle shouldn't be independent of De Broglie's relation of momentum to wavelength. We use wavelengths to measure distances. Whenever we measure distances, we quantize an unknown distance with our measuring apparatus which communicates its quantized result to us as a rational number times 1 + or - i × delta. A distance along x axis is measured as x - i dx or x + i dx where i is √-1.

[@alokverma3311]

WONDERFULL LECTURE...SIR YOUR LECTURES ARE CHANGING MY LIFE

[@lecturesbywalterlewin.they9259]

:)

[@alokverma3311]

thank you sir .....................but sir how will i develop an amazing teaching power just like to you that i can impress everyone and makes fiziks lectures more interesting......sir please suggest me a way that i can take the the admission in MIT.

[@lecturesbywalterlewin.they9259]

How to get into MIT? kzbin.info/www/bejne/noPTZIF6Yst1hNk

[@toddprifogle9911]

sir, as you say the orbital concept is a misconception. . however the path of an orbital body will appear as a wave over time . I only mention this to imply the effect of eclipse on the appearance of the tracked path could be seen as pulses of a waves or packet or quanta ...

[@karlpages1970]

thanks...It is good to remember and understand these principles of QM. Because eletrons have a lot to do with chem and bio ; hence, aging and sickness.....

[@lecturesbywalterlewin.they9259]

:)

[@bangla-sydney]

I wonder what will happen if we restrict photons in both x and y directions. Will we see a cross or a disc of light on the wall?

[@sarvesh_soni]

Really Explanation... Thanks a Lot... 💗

[@yashlokare5386]

Oh, I see. Thank you for the clarification, Professor Lewin.

[@Amansarkar700]

Nice lecture i have ever seen in my life

[@stevebutrimas9972]

The principle is a Clear consequence of definitions but it seems that somehow somewhere sometime we have knowingly or not seen into the secrets of the universe.

[@junkerzn7312]

I knew this but I couldn't turn it off! I immediately went onto Amazon and bought a bunch of of diffraction gratings for the kids :-)

[@lecturesbywalterlewin.they9259]

great!

[@darshansonagara5759]

love you sir i can finally understand what will be happening in this ..... but i did not understand the experiment that's was perform by you in the last.

[@williamtachyon2630]

What do girls shout when Walter Lewin declares he loves physics? ”Me too!”

[@lecturesbywalterlewin.they9259]

ha ha ha

[@williamtachyon2630]

Jokes aside. You were one of the reasons I applied to a university to study physics. Your lectures are so good, far better than any other lectures I've seen. Greetings from Finland!

[@lecturesbywalterlewin.they9259]

:)

[@rebokfleetfoot]

i never understood Alberts conundrum with it, clearly the photon travels as a wave and interacts as a particle

[@mohammadyaseendar700]

u r the best physics pro sr i have ever seen

[@jjrb230]

Complex (strange, abstract) things explained in a very interesting way. Now you can pause the class, Print screen, rewind, and above all you don't have to pass any exam. You can even brag: Last night? Oh "I was studying the Heisenberg principle at the MIT"

[@lecturesbywalterlewin.they9259]

:)

[@jjrb230]

Your lecture was great Sir I am a stroke and brain tumor survivor but still capable of following what you said; I will have to review it because my temporary memory was damaged (by the stroke) but I understood you and even enjoy it! The historic perspective helps a lot to link the concepts.

[@lecturesbywalterlewin.they9259]

That's GREAT!

[@ThomasHaberkorn]

great lecture. I bought a grating after this

[@obayev]

What a pleasant dive into the microworld!