MIT 8.04 Quantum Physics I, Spring 2016 View the complete course: ocw.mit.edu/8-04S16 Instructor: Barton Zwiebach License: Creative Commons BY-NC-SA More information at ocw.mit.edu/terms More courses at ocw.mit.edu
КОМЕНТАРІ: 1 400
@andrewchen26734 роки тому
See you all next year when the algorithm brings us back
@MrSpaceCrunk4 роки тому
Andrew Chen Hahaha had to laugh so hard!
@CarlosGomez-lp9zi4 роки тому
Hi bud
@khaledadrani31844 роки тому
It actually did. Interesting.
@gheorghegeorgescu78464 роки тому
I will be reliving this comment in 6 months time again
@kartikrathore57204 роки тому
@@iiwi758 when it was in my recommendation I thought "this is something interesting to watch" But in comment section I had already liked the top 2 comments.
@m.raedallulu41664 роки тому
7:00 (When very good physicist are wrong, they are not wrong for silly reasons, but they are wrong for good reasons, and we can learn from their thinking.) I love it!
@eloymarquez47834 роки тому
Booom
@larrykinglk4 роки тому
Love it too. Very inspiring!
@jasonsmith41144 роки тому
When something sounds right but is also actually right, great quotes are made.
@TruMystery4 роки тому
stfu brainlet
@declanwk13 роки тому
Einstein was not saying that QM was wrong, it gives such accurate answers it can't be wrong. He was saying that QM was incomplete. Bohr's dominant personality resulted in history recording that Einstein lost these early arguments in the interpretation of QM but many of the questions he raised are still unanswered and need to be resolved along with incompatibilities between QM and GR.
@stm32526 років тому
gauss hated the name imaginary, because it's confusing.He suggested to use lateral, because the complex number are represented on the lateral axis unlike all other numbers.
@ridovercascade45514 роки тому
He sounds right, but I am not to deep in Algebra to have an opinion. Maybe Imaginary has also some point of truth? The square root of -1 is impossible, so imagine being possible. B times that imaginary square root -1. But sure for me as a student, it would be made me so much clear if it wasn't called imaginary axis.
@Adam-rt2ir4 роки тому
It's impossible in the usual high school restriction to real numbers, but then people starting to study complex numbers complain, because why study something that is impossible/imaginary, it creates a bad approach, not very open minded.
@BlahBlahBlah136234 роки тому
@@ridovercascade4551 'imaginary' numbers are as imaginary as negative numbers.
@roc65964 роки тому
i can be easily defined as the product between to points in a Cartesian plain which is (0;1).(0;1)=(0;-1) looking at an Argand Gauss plain it would look like i.i=-1, so we can basically multiply to real points and obtain minus one
@Jack010104 роки тому
@@ridovercascade4551 Actually imaginary numbers are real, so it's better call them "lateral"
@ramenmondal83423 роки тому
I am not mathematics major. But whenever I watched videos regarding math it brings Peace in heart. I don't know why
@chiranjitray760Рік тому
That makes you a mathematician
@antoniodiaz1998Рік тому
That's because mathematics is a gift from god
@ergbudster333311 місяців тому
Change your major. Unless you're physics or stats or social science with stats then you already in place. Continue thinking. Be the genius you were meant to be.
@zTheBigFishz11 місяців тому
Music of the Spheres...
@suyash-dwivedi11 місяців тому
Well you feel nostalgia, that's why.
@luismontalvohiroyasu58144 роки тому
Barton Zwiebach is peruvian. He was born and studied school and electical engineering in Lima, Peru. As a peruvian I feel so proud of him.
@felipetoledodiaz19284 роки тому
Que orgullo, saludos desde chile
@mauricioaletz96944 роки тому
Wow, increíble que haya llegado tan lejos!
@umeriqbal54064 роки тому
Peruvian flake cocaine 👍
@dibujodecroquis16844 роки тому
Ya me di cuenta de que su acento al hablar inglés es de hispanohablante, pero ni su nombre ni su apellido son de hispanohablante...
@luismontalvohiroyasu58144 роки тому
@Arriaga Two El Perú es un país compuesto por un crisol de razas: mestizos, nativos, blancos, negros, asiáticos, etc. PERÚ: País de cultura milenaria y de todas las sangres.
@codeisawesome3694 роки тому
If I ever strike it rich, I would love to go to MIT to study physics at leisure with amazing teachers like this...
@VoidFame4 роки тому
Tbh you could just go for free and not get credit. Make friends not money :p
@codeisawesome3694 роки тому
@@VoidFame I'm not from the States, so unfortunately I'll be stopped at the border even though I'm trying to make Friends - because I don't have Money...
@VoidFame4 роки тому
@@codeisawesome369 I see now. It's not an issue of tuition, but an issue of living arrangements. I wish you the best of luck if you decide that is your pursuit.
@codeisawesome3694 роки тому
@@VoidFame Thank you! :-) Have a great week ahead.
@0xDEAD_Inside4 роки тому
@@VoidFame What! You can?
@stephenanastasi7483 роки тому
I had to learn this by distance education (1992) before the internet and always struggled. Barton makes it seem so easy. What a fabulous lecturer.
@vahidmirkhani4 роки тому
I clicked because I thought he was a young Harrison Ford. Now I know how complex numbers are crucial part of wavefunctions in quantum.
@eklipsegirl3 роки тому
Who the fuck is that Harrison Ford? Why are people so obsessed with screen clowns and disregard quantum physics? I had to google to know who that guy is and was very disappointed to find out that it's yet another random film actor :(
@omniyambot98763 роки тому
@@eklipsegirl yeah useless actor
@NightmareCourtPictures2 роки тому
@@eklipsegirl Relax. Some of us that like physics, also like movies. In fact some of us like physics because we picked it up from watching movies! Twister was one of the first movies i saw as a kid...I largely believe that this movie alone is one of the things that shaped my entire life to who I am today, being both a filmmaker and a hobbyist physicist.
@melontusk73582 роки тому
@@eklipsegirl chill, mate, nobody's disregarding QM here. As a physics major who minored in other things, I love cinema. "Blade Runner" starring Harrison Ford was a bold film that dared to ask thought-provoking questions. "Interstellar" is another cerebral masterpiece that also deals with existential ideas as well as Theoretical physics, mainly General Relativity and higher dimensions. It truly sparked my interests again and inspired me to retake my Relativity course. Films have influenced many great physicists and engineers in real life, most notably Hyperspace in Superstring Theory and most recently the NASA's warp drive from "Star Trek" by Alcubierre.
@arnabmukherjee61922 роки тому
@@eklipsegirl calm the fuck down you pseudo intellect
@manuelignaciodelgadotalave79585 місяців тому
As a peruvian I feel proud of Barton, he is the best student of the National Engineering University in Lima Peru
@user-tt2po5wg7n4 місяці тому
What a great introductory video. The professor is comfortably understandable and thorough.. Fantastic, short introduction to complex numbers and their importance. Thanks for posting!.
@timthompson4684 роки тому
Great video. I’m reading Ruel Churchill’s book on complex numbers and applications. I like his introduction. Instead of starting with the definition of i as the square root of negative one, i is introduced as part of a function that is necessary for certain equations (an ordered pair with certain, somewhat unusual mathematical properties). As, I read it, the fact that it turns out to be the square root of negative one is more a consequence of the definition , rather than the basic definition of i. It’s a subtle point, but that explanation sits better with me. Most modern books start with “i is the square root of negative one,” and that’s harder to get my head around than the more fundamental definition.
@fourier07able4 роки тому
'I' is a solution of the equation: x^2+1=0,so we could take this equation as the generator of imaginary numbers, i.e. the positive square root of '-1' is the imaginary unit i=(0,1), an ordered pair.
@akinyiomer45894 роки тому
This is actually so damn useful. I wish more instructors/professors/reference books approached the more abstract concepts from this perspective, as the majority of learners - particularly those who don't enjoy maths - will have a better chance at getting a complete and thorough understanding.
@xqamii38624 роки тому
most of the reasons it is introduced like this is because it was used by him previously in the lecture, when talking about Motion in 1D, i think. i do agree that it is a good way at looking at i, and complex numbers as a whole instead of just defining it by itself
@TheBeatle494 роки тому
Agreed!
@MGHOoL53 роки тому
Exactly! That's how we should learn: why was a concept created and not 'here is a useful information to remember'. Things must be learned as they arose: out of necessity not possible utility. That's why I find it fascinating to read history which renders the present necessary or in hermeneutics (e.g. psychoanalysis) to grasp things from their fundamentals.
@Avicenna1011 місяців тому
Fantastic, short introduction to complex numbers and their importance. Thanks for posting!
@hugoaraujo3Рік тому
I am a teacher at the beginning of my career. That was a very inspiring explanation.
@andrealeto995 місяців тому
you teach in university?
@LsPl.11 місяців тому
Honestly, this was probably the best introduction to quantum mechanics i'ver ever heared. Before you get to this whole superposition shit and stuff, first explaining the fundamental maths behind it, which by all means isnt that hard to not teach it to students. Great job.
@mohamedaminechekkouri88903 роки тому
I’m actually an engineer but this is the first time I understand why we really need the complex numbers Thank you sir !
@nyahhbinghiРік тому
He didn't really get to a full explanation but it was a good start...a couple of identity equations doesn't explain at least for me
@leif1075Рік тому
EXSCTLY ZHE DIDNT EXPLAIN AT ALL WHY WHY DOES TJE WAVEFUNCTION have imagonary i in there to begin with...it has partly to do with not being bale to have time move backwards but he doesn't get into that at all..
@michaelgoldsmith9359Рік тому
We don't need complex numbers it's just a simple way of taking into account things which change with regards to the period of sin function, like ac current, or for simplifying manipulations of vectors, which can be done without complex numbers but just in a nightmarishly complex way.
@kuldeepshukla179711 місяців тому
Started with x^2 + 1 =0. People were not used to with these kind of equations
@iamthegreatest391411 місяців тому
Pure Mathematics don't search for Its applications. Pure Mathematicians do mathematics for fun & they get pleasure doing it . For example - Group Theory was Invented for Fun . But later other people found its uses in Computer Science & Quantum Physics
@usptact3 роки тому
Very nice short note on complex numbers. A great professor tells you much more than just writing down those dry equations.
@afifakimih88234 роки тому
Very pure very clear very quality lecture series on QM and QFT...!❤💜❤
@espi33244 роки тому
This brings me back to the good old days of engineering school. Ironically I miss it. I felt so sharp in my mathematical skills.
@keen24614 роки тому
When I studied this subject 25 years ago, back on the engineering classes, I remember I got to understand the topic quite well as it was necessary to solve circuits problems. But I never got to use that on the real world, and now it is a "complex" concept for me. Anyway, I hope someday I have the time to brush up on my advanced maths.
@shameelkhan81892 роки тому
Oh jee aspirant!
@nathanwalker14243 роки тому
What a great introductory video. The professor is comfortably understandable and thorough.
@YakiOnigiriZoro4 роки тому
I thought that was Harrison Ford in disguise
@camunoz24 роки тому
Yeah right?
@gabor62594 роки тому
Harrison Ford + Benedict Cumberbatch
@pugboi80174 роки тому
ROFL
@PeopleOfCasinos4 роки тому
Lol I had the same thought "wtf is Harrison Ford doing at MIT????"
@anderson.barcellos4 роки тому
Dude! Tot's! 🤣
@ezomaruzcategui8011 місяців тому
Thanks for the contribution. Make remember My times in Electrical Circuits with Samer Teacher.
@zzzyzzzyzzzyxxx3 роки тому
It is a tragedy that the terms _real_ and _imaginary_ were adopted to classify these numbers since: a) The origin of the terms was actually meant to be used as an insult to certain mathematicians (more in a moment), and b) It confuses students learning math who, through no fault of their own, assume the lay, or common, definition of imaginary, that being something that is “fantasy”, “make-believe” or “made up”, leading to a student’s understandable conclusion: _how can something that “doesn’t exist” be in any way useful? _ Good question! Origin and usefulness to follow, but first . . . . A side track in nomenclature . . . . In physics, there is a fundamental particle called a quark. There are 6 types of quark. These types are called flavors. The flavors of quarks are: up, down, bottom, top, strange and charmed. Why is one strange and the other charmed? Can you really taste them if they are called flavors? Nope - they are just names whose origins come from the imaginations of the physicists involved. (en.wikipedia.org/wiki/Quark#Etymology) *The origin of the terms Real Number and Imaginary Number* In the late 16th to early 17th century, when some mathematicians began developing the idea of the square root of negative numbers, other mathematicians were not too impressed. One prominent mathematician (and naysayer) of the day was Rene Descartes, who wrote, scathingly, "_These people play with their imaginary numbers while we mathematicians work with real numbers_." Herein lies the origin of both terms real and imaginary. Yes, before Descartes remark, the numbers we now call real numbers were not called real numbers by mathematicians, they were just called numbers!
@beoptimistic58533 роки тому
ukposts.info/have/v-deo/kIF6lqRpbpqAy3k.html 💐💐💐
@lolaalsaadi57084 роки тому
Wow , such an amazing explanation, thanks lot
@sungbeomcho36065 років тому
How couldn't I thumbs on this lecture. Thanks professor
@cidorodrigues60874 роки тому
I'm Sido Rodrigues Brazil I really like Quantum Physics Classes. Very important to know quantum physics. Teach everything the universe knows and you gain self-knowledge about everything. Great series of really useful lectures on quantum mechanics. I am also very grateful to MIT OpenCourseWare and Barton Zwiebach... etc...
@puekai4 роки тому
I like his writing, elegant
@Rocket89P13.11 місяців тому
El legendario Barton de la UNI
@gauravxsharma4 роки тому
I really love it we need this type of teacher in india because I always think why this is required to study and he had a very clear point of it with examples i love it never in my life i had this my clear view to any chapter a lots of love from india.
@beoptimistic58533 роки тому
ukposts.info/have/v-deo/kIF6lqRpbpqAy3k.html 💐💐
@souvikdas56624 роки тому
Really awesome explanation of complex nos and necessities in qm
@EeshwarBalageethavengateswaran4 роки тому
4:24.. yes we can work and get it.. McLaurin's series is one best way to use and prove that e^ix = cos x + i sin x.. U can enjoy proving it bcoz it gives a detailed and satisfying proof. I've done many times.. it's interesting.. 😊😊😊
@xyzct3 роки тому
The most enlightening way to teach complex numbers is to show the student that from N to Z to Q to R to C is merely four different quotient set extensions designed to remove the obstructions to the inverse operations: subtraction, division, logarithms, and root extraction, respectively.
@LarryD-ul3le11 місяців тому
You mean limits, not logarithms. And you should really continue on to quaternions.
@xyzct11 місяців тому
@@LarryD-ul3le, no, I do not mean limits. I mean logarithms. And tell me, what obstruction to an algebraic inverse operation did the quotient set extension to form quaternions remove?
@rafanifischer31524 роки тому
These are cool studies. The professor has a nice clear-cut way of explaining without overemphasizing the simpler parts of the mathematics.
@thegirlwholovesmaths4 роки тому
Totally agree. Clear and concise. He knows his stuff.
@rogerarrick19076 місяців тому
Oh that was very good. Brought a lot of stuff together nicely.
@pietro52665 днів тому
Because of this lecture, I now understand the foundation of cos x + i sin x, and also how "i" came to exist and it's usefulness. Never saw these explanations before.
@naveenkrupadas63333 роки тому
MIT is MIT. It is always absolute. Thank you, MIT
@beoptimistic58533 роки тому
ukposts.info/have/v-deo/kIF6lqRpbpqAy3k.html 💐💐💐
@pandit-jee-bihar4 роки тому
He summed it all up with the statement that "complex number was needed to solve equations". That's it!
@guythat7794 роки тому
That's a shit reason my nigga
@RangerCaptain11A4 роки тому
शास्त्र ध्वनि - Recorded Scriptures right, imaginary numbers are for completeness. that is a huge reason.
@ffggddss4 роки тому
@@RangerCaptain11A Yes, exactly, and that goes deeper than just needing them to solve equations. Complex numbers, "complete" the real numbers, in a strong sense. Even as needing them to solve equations opens the door to their existence. Fred
@pandit-jee-bihar4 роки тому
@@ffggddss 'Complete' or 'Completeness' Is it something empirically defined or more of a feeling ? Does Integer complete whole number ? The reason one part of it is called is called imaginary is because well it's really imaginary and came into being as a notational convenience for mathematicians. It's a great imagination and opens door to solve equations which could not be solved before.
@ffggddss4 роки тому
@@pandit-jee-bihar Well, no, it wasn't meant in any formal sense. And yes, integers (ℤ) could equally well be said to "complete" counting (aka, natural) numbers (ℕ); as do rational numbers (ℚ) for integers; as do real numbers (ℝ) for rationals. And in each case, there's an in-built operation in the original system, that generates the extended one: • subtraction (inverse operation of addition) extends ℕ → ℤ • division (inverse operation of multiplication) extends ℤ → ℚ • limits of convergent sequences extends ℚ → ℝ • exponentiation extends ℝ → ℂ ( [-1]^½ , e.g.) The same could not be said for the quaternions, e.g. Perhaps the most compelling case for complex numbers is that, on the real line, not every differentiable function is analytic; in the complex plane, a function can't be differentiable without being analytic. Basically, in the complex plane, the constraints imposed by differentiability suddenly become much more stringent than those on the real line. Fred
@FunPHYSICZ9 місяців тому
This is excellent. One of my degrees is in Physics. I have a lot of math in my background. Complex Numbers were a necessary subject in order to do the math. The problem was that the concept of mapping complex numbers to a Cartesian Plane was just presented as a given, with absolutely no explanation why. "That's just the way it is." Dr. Zwiebach does a much better job of presenting the "why" than most professors. But the ultimate understanding for me occurred when I stopped and read the history of Rene' Descartes, one of the greatest mathematicians ever, and the reason we call this plane representation "Cartesian". If you get an understanding of Descartes's thought process and where the concept of Complex numbers comes from, you can think like a mathematician and not just depend on memorization.
@tchevrier9 місяців тому
complex numbers are fundamental in electrical engineering and pretty much anything that deals with waves because that angle gives you a way to represent the phase of the wave.
@spb11793 роки тому
Going to have to watch these lectures, this prof is amazing
@gokurocks94 роки тому
I took a lesson on complex numbers before I took any trig, Calc. I didn't know you could use i to solve polynomials. That's incredible...
@drania764 роки тому
That’s the correct order of learning mathematics, congratulations. Once the idea that only positive number has a root square has been internalised it really is difficult to understand complex numbers and complex numbers are another level of mathematics and that is a real magic.
@stephenbeck72224 роки тому
The primary purpose of complex numbers in algebra is to solve polynomials. How do you solve x^2+1=0 without i?
@no_more_spamplease512111 місяців тому
@@stephenbeck7222 Yes. Complex numbers were invented to ensure the *closure* property for solving quadratic polynomial equations, ensuring any of them will necessarily have 2 complex roots (which can be real numbers or not).
@stassavchuk3 роки тому
Well, finally, on the 27th year of my life I realized the physical sense of the complex number :)
@srinivasg12954 роки тому
Hats of to the instructor.. Amazing brain people have.. So complex
@ilmdost80884 роки тому
Love this, such a nicely interpretate, We really need of such great man as an teacher.
@beoptimistic58533 роки тому
ukposts.info/have/v-deo/kIF6lqRpbpqAy3k.html 💐💐💐
@springdoctor4 роки тому
There is no mystery about imaginary numbers or euhler’s identity. As the exponent of e , the imaginary number causes the radius to rotate counter clockwise around the x, y axis of the unit circle sweeping out out cosine and sine values just as the good professor says. Knowing this, imaginary numbers make perfect sense and e to the i 2pi = 1
@jonahansen5 років тому
Man, this professor is good!
@NeoCynic110 місяців тому
Reading Spengler and his explication of the various "mathematics" of different Cultures. This helps
@MikeDbean4204 роки тому
Great teacher. Thank you for video.
@roughsharkangular20344 роки тому
I clicked because i thought it was harrison ford teaching mit class
@FernandoVinny6 років тому
Obviously MIT students already know what are Complex Numbers
@MetallicDETHmaiden5 років тому
you'd be surprised.
@mohittiwari89345 років тому
Yes
@aperture04 роки тому
@Non sum dignus I had to 'cause it's freaking MIT!!!!
@brandonklein14 роки тому
I agree, but perhaps it is the case that thinking of them in maybe a new more pure way as described by the professor gets some of the clutter and possible confusion about them out of mind.
@smishdws4 роки тому
At my school, introductory mathematics is a prerequisite for quantum mechanics, but I think complex numbers was still very briefly discussed. Always good to quickly put everyone on the same page to follow discussion, and emphasize some important math concepts that will connect to physics concepts later on.
@vipuljani60273 роки тому
I am first time meeting with Walter Levin in IIT Bombay and this time I see that professors is no difference between that!!! I love tham very much in this time I am in harverd in us I am very happy too
@nizarsurche4 роки тому
شكرا على التقديم الرائع
@richardhall98154 роки тому
I love how the chalk boards move up and down like window sashes.
@andrewlankford96344 роки тому
You know it's MIT when every blackboard moves up and down like a window sash. That's reeel quality there.
@plfreeman1113 роки тому
A great professor hints at things beyond what are being taught. @2:30, "It's actually zz*, a very fundamental equation". And with year's of math under my belt now, I'm like, "Oh, man, that is a huge deal." That you can use the multiplication of a complex number with it's conjugate to get a real number that is a squared norm and generates a measure on the space of C. Mind still blown (even though I know this stuff well). But the professor just moves on and leaves it lying there. Quietly acknowledging the importance, but knowing that it's a distraction from what needs to be taught. Bravo.
@dkarthiganesh4 роки тому
Thanks Professor
@oprahwinfrey2967Місяць тому
Historically, there was sequential extension of number fields. The field of natural numbers was extended to the field of integers, then up to the field of rational numbers, then up to the field of real numbers and, at last, up to the field of complex numbers. The complex field thus has a key distinctive feature: It is algebraically closed. Restriction of physical quantities only by the field of real numbers seems logically unsatisfactory since mathematical operations often deduce them from the field of original definition.
@jaacobb1234 роки тому
When you're smart like these professors you can convey as much information speaking slowly as eminem rapping
@dozog4 роки тому
I like your observation. It's about the information density of this prof.'s words. An involved receiver is also a requirement. Eminem videos have more views.
@jaacobb1234 роки тому
@@dozog Exactly, and very true.
@dozog4 роки тому
@@jaacobb123 If the old adagium that repetition is the mother of learning is true, then rappers may still be great teachers.
@pre-universitygeometricalg586211 місяців тому
In Geometric Algebra (which is a development of Clifford Algebra), the unit imaginary is given a geometric interpretation that is extremely useful in formulating and solving mathematical problems that arise in a broad range of fields, including quantum mechanics. Our channel is mainly for lower-level users of GA, but some of the members of our associated LinkedIn group are GA experts, and will be happy to direct interested viewers to sources of additional information.
@tenaciousgirl52014 місяці тому
Sir, you don't know how grateful i am to you ! May the One True God bless you.
@shubhambaidya61263 роки тому
Such good quality education to millions around the globe... *Claps claps*
@JeffaHensley4 роки тому
Decent lecture, but it begs the question of the title of the video. He just states that they’re necessary, meanders around a few examples of how we’d be lost without imaginary numbers, but other than this necessity for their existence, doesn’t explain them.
@kingk.crimson66334 роки тому
"Other than the necessity for their existence" that is the title of the video
@RangerCaptain11A4 роки тому
probably a 1.5 hour class, so most of the content is missing.
@ramenbroth4 роки тому
You're asking for something that's not within the context of the title of the video...
@madScientist4044 роки тому
the answer to your question lies in Geometric Algebra. The result of the work of Grassmann, Clifford, Hamilton and sort of rediscovered by Hestenes. It gives you a geometric interpretation for the equation i^2= -1. It can be associated with some plane in physical space.
@flumpyhumpy4 роки тому
@4:38 "Complex numbers, you used them in electromagnetism, you sometimes used them in classical mechanics, but you always used them in an _auxiliary_ way. It was not directly relevant because the electric field is real, the position is real, the velocity is real, everything is real. And the _equations_ are real. On the other hand, in quantum mechanics the equation *already has an i* . So in quantum mechanics, psi is a complex number. _Necessary_ . *It has to be* ." This lecture is from a course on quantum mechanics. The title of the video is apposite, concise, and absolutely correct.
@peterpetigrew28694 роки тому
"GET TO THE CHOPPER !!!" 😂😂😂😂
@sneakytweeky76253 роки тому
Awesome teacher he really speaks a story which makes it attractive to listen to Wish my teachers spoke like this
@beoptimistic58533 роки тому
ukposts.info/have/v-deo/kIF6lqRpbpqAy3k.html 💐💐💐
@faustdownunder4 роки тому
The "norm" is otherwise also denoted as the magnitude of the complex number vector. May I respectfully add that Z = cos(theta) + i * sin(theta) only if magnitude(Z) = 1. Complex number are used and have been used for a very long time in AC circuit theory. We can indeed very well measure complex numbers by simply measuring amplitude and phase of voltages, currents, field vectors.
@98danielray4 роки тому
he said the unit circle
@joefagan93355 років тому
Well that was begging the question!!!
@emmanuelb.jankpolo46515 років тому
Great teaching
@peterkiedron89498 місяців тому
Do not confuse notation with deeper meaning. The equation can stated as a set of two equations of Re and Im parts and complex numbers do not have to be invoked. So, no complex numbers are not necessary but they simplify notation.
@fethilakhdari10784 місяці тому
Great video in every respect, please keep them comming.
@Tomahawk19994 роки тому
if i had teachers like these, maybe i would not have hated math so much and actually done well in my life.
@AnimeCritical4 роки тому
Even now it's not too late.
@MaxPower27194 роки тому
Many people who had bad or mediocre teachers turned out really well. Your future lies in your own hands, not in the hands of some teacher. All the tools are available; you choose to pick them up or walk away. If the "1999" part in your name reflects you year or birth, you are a measly 20 years old. Your life has hardly begun. You have all the opportunities ahead of you to "do well" in your life. Or, you know, you could just sulk on in the internet and blame others for not following your hopes and dreams.
@stuartyeo53544 роки тому
Very encouraging :)
@thicclumber57904 роки тому
Tomahawk1999 ur a failure because of urself and nobody else, but sure blame ur teacher if it makes u feel better
@felipeteixeira71694 роки тому
thicc lumber who the fuck are you to judge someone as a failure, though? There are n factors that may cause one to get unmotivated and bad teachers is surely one of them.
@ffggddss4 роки тому
This is really well presented! This guy ought to be teaching at MIT or the like. Oh, wait, ... Fred
@amitabhbasu65834 роки тому
Flfoilm
@remixex36911 місяців тому
I have never taken QM. However, thanks to QM we have a very VERY robust wave propagation theory. One of the most reliable ways to compute synthetic seismograms is through Normal Mode Summation. It saves you a lot of headaches to do this!
@Larry0008 місяців тому
G.O.A.T. explanation of complex numbers!
@AndreaCalaon734 роки тому
I would love to eventually hear about Geometric Algebra ...
@RangerCaptain11A4 роки тому
my professor for that class was romanian. she talked slow like this professor, so it was easy to follow. it was a good class to expand your mind.
@AndreaCalaon734 роки тому
@Muhammad Haider No, I mean "Geometric Algebra", as proposed and first studied by David Hestenes
@NLGeebee4 роки тому
Except that i ≠ √-1. By definition i² = -1, so if anything i = ±√-1.
@adrien85723 роки тому
No by definition i=(0,1)
@NLGeebee3 роки тому
Adrien If you mean that the coordinates of z = 0 + i in a complex plane are (0,1) then you are right, but a graphical representation is not equal to the definition.
@adrien85723 роки тому
@@NLGeebee The way complex numbers are built is by defining two operations on the set R^2 : one addition and one multiplication. i is a notation for the couple (0,1) because it is easier two manipulate this notation. It really is just that. You can represent all complex numbers in R^2 because they are just R^2 with two operations !
@NLGeebee3 роки тому
Adrien I believe I was tought that if the complex number z = i, or z = 0 +1i, then that number z is represented in R² as the point (0,1).
@adrien85723 роки тому
@@NLGeebee That is indeed true !
@Alpha-wj9hb3 роки тому
الراجل ده عالي فشخ ❤️
@dearheart27 місяців тому
Brings back memories.
@williamsmith42204 роки тому
He just derived de moivre's theorem!!! Holy cow I never noticed that.
@puru18184 роки тому
No, he didn't...
@SuperSaltyFries4 роки тому
He derived Euler's formula.
@p27kushagra4 роки тому
@@SuperSaltyFries He derived nothing. What's wrong with u people..?
@Indic4Zone3 роки тому
i should really stop binge watching science videos when i keep saying "alright just one more yt videos, and i will sleep after this"
@flowerwithamachinegun26923 роки тому
r/iamverysmart ?
@Indic4Zone3 роки тому
@@flowerwithamachinegun2692 nah dude, i'm just wondering why these lectures videos keep appears in my reccommendation, yeah sometimes i do watch 3b1b/blackpenredpen/welch labs/ocw but most of the time, i watches family guy/simpsons/futurama/one piece/the last airbender, i just like to do it, i'm just not very sure why this video keeps appearing in my reccommendation
@memojedi4 роки тому
Perfect explanation! Just perfect!
@beoptimistic58533 роки тому
ukposts.info/have/v-deo/kIF6lqRpbpqAy3k.html 💐💐💐
@maggiejetson79049 місяців тому
I always wonder why we need to learn complex number, but didn't understand it till 3rd year in college for electrical engineering. It makes frequency related work a lot simplier.
@oldguy1958hk3 роки тому
Good refreshing course... I make living on I... I call it "j" part of a number ...for me I stands for current, I m an electrical engineer.
@davjdprjce3 роки тому
the imaginary unit is denoted *j* in electrical engineering since *i* denotes current
@afifakimih88234 роки тому
Who says physics is boring...It's actually amazing...just see these lectures.!!absolutely Amazing.!"
@kandasamym660011 місяців тому
Knowledge should for knowledge only but not exami orientation The teacher is teaching very nicely
@spacelemur79559 місяців тому
All my life from ~ age 10, when in the presence of a good teacher I have always felt on the verge of understanding math, but have never had it quite click into place. Next year I turn 70, and am still trying, albeit with declining hope.
@schmetterling44778 місяців тому
Why are you telling us that you never had the intention of paying attention to mathematics? ;-)
@kylewhitney28903 роки тому
While the smartest of the smart get into schools like MIT, Harvard, etc., I’d love to go there I would sit in on lectures like this for fun.
@TheMounten13 роки тому
If you work hard enough you can get into a good uni in the us with comparable education although you may have a large debt to loans
@CIOWhitepapers3 роки тому
That's what you're doing right now. Many of the big universities have full classes on youtube now and it's quite possible that you'll get more from those courses than the freshmen who pay top dollar to attend in person.
@stevenvanhulle72424 роки тому
"Once you invent i you don't need more numbers." Quaternion: "Am I a joke to you?"
@maxfrankenberg82604 роки тому
Steven Van Hulle ... to solve any polynomial equation
@ema79564 роки тому
my favourite staff.i love maths
@AkashGupta-yq8lx4 роки тому
I love complex no.. as well as complex geometry❤️❤️
@2002tantry4 роки тому
Does anyone else feels like you understand these things way down in your career and it just went above your head when you were actually learning in college 😂?
@SuperSaltyFries4 роки тому
It's no surprise. We hardly have any time in university to actually read the damn textbook because each professor assigns so many homework assignments each week plus the 3-4 lab reports to complete.
@eceakyol58576 місяців тому
in turkiye we learn the complex numbers in highschool
@jelteverhoeff14 днів тому
In NL we learn nothing in highschool
@Shrodinguer432112 днів тому
Come and take a look at the moroccann program 😂
@ansupriyadarshi145611 днів тому
So do we in India. It’s a fascinating subject when you look back at it. At the time I thought why study when it’s all imaginary 😂
@t_aikutsu11 днів тому
In the UK usually people would start to learn it in university, but some people choose to study "further maths", which sees them learning about complex numbers from 16
@rs32410 місяців тому
awesome professor!
@donwald343610 місяців тому
MIT has the best blackboard erasers, that big boy is a dream.
@patrickryckman38674 роки тому
Wow Harrison Ford can do anything.
@jadghalayini14466 років тому
What if we had two numbers z1 and z2 such that z1 != z2 but |z1|^2 = |z2|^2 (trivial example: z1 = 1, z2 = i). If what we're interested in is the norm squared, when it comes to measuring in quantum mechanics, then what is the difference (measurable, perhaps) between z1 and z2? Another property?
@James__1236 років тому
I remember this being answered in my lecturers last year, but I can't remember the answer :D I'm sure he's going to mention it later in the course
@IgorAherne6 років тому
I believe it's the "cosine similarity"
@zoltankurti4 роки тому
Good question. The answer is, you can't measure the phase alone. But if it interacts with another system, the phase difference between the two systems can be measured, roughly speaking. The interference pattern of two waves for example will depend on the phase difference of the two waves. And it's similar for all other systems, you will get an interference term in the prediction which depends on the phade difference and can be measured.
@memelsify4 роки тому
Look up Aharnov-Bohm effect.
@zoltankurti4 роки тому
@@memelsify you still need interference to measure this effect, this is not usable to measure the phase of the wave function. You always need interference with another system for that.
@jadenmax6794 роки тому
great teaching.
@erniewinn24154 роки тому
He is a great lecturer.
@StudiesBR4 роки тому
what kind of harrison ford is this?
@tropictom59964 роки тому
The one that is starring in the upcoming math adventure film “Raiders of the Lost Quark”
@novemberalpha60234 роки тому
Indiana Jones at University
@GaganGrewalf0954 роки тому
Imaginary
@MaheshKumar-dn2hb4 роки тому
0:01 Is nobody going to talk about how he wrote "couplex #'s" instead of complex #s?
@gauravbanakar84344 роки тому
nope.
@vicheakeng68948 місяців тому
#DATA
@Cjnw5 місяців тому
Pedantic perspective
@arifulmoral8 місяців тому
Excellent
@user-it9tf6wf9e8 місяців тому
i love this!!!
@tonypower56254 роки тому
Ummmm Harrison Ford teaching complex numbers...must be his next movie!!!😂😂😂😂