Lecture 3: The Wave Function
Вставка
- Опубліковано 17 чер 2014
- MIT 8.04 Quantum Physics I, Spring 2013
View the complete course: ocw.mit.edu/8-04S13
Instructor: Allan Adams
In this lecture, Prof. Adams introduces wave functions as the fundamental quantity in describing quantum systems. Basic properties of wavefunctions are covered. Uncertainty and superposition are reiterated in the language of wavefunctions.
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu
Big up to MIT for offering these OCW lectures. I have learned Calculus, Classic Physics, Linear and Abstract Algebra, and Quantum Physics and I didn't even have to pay late library book fees. 👍🏾 Thanks MIT, for being conscientious and gracious! 🎉💥🪅🎇🤸🏽♂️🕺🏿💃🏼🎆🎊🙏🏾
Amazing !
i think this kind of high quality content makes the world a better place for seekers.
First you need to find it though. If you haven't figured out the value of science and scientific institutions yet you might end up "learning" "quantum mechanics" from "what the bleep" or Deepak Chopra, instead of learning it from MIT.
The truth seems to be, that for many people it's hard to get on the right track without some type of guidance. They'll get sidetracked by conspiracy theories, fraudulent claims and various pseudo-sciences. And that may be understandable, since we haven't evolved to perceive or understand reality accurately. Furthermore our success (as a species) seems to be largely based on an accumulation of knowledge i.e. learning from other people and building upon that. So it's understandable that people can not see the value of the scientific method or scientific institutions. Scientific thinking isn't something, that has come naturally to us. It's not something that people just come up with themselves. So for most people it requires a person, who introduces them to science, leads them into the right direction, makes them ask the right questions etc. If you lack that you might not be very likely to end up here.
You obviously missed this: 53:13. Think about it.
@@stauffap 4 years after my comment I'm not really any further with this lecture series. But started multiple other lectures on different topics like Human Behavioural Biology from Stanford.
I'm also thinking of finally trythe problem sets, but I guess I maybe would be hit by a wall then. So I probably gonna try it anyways.
@@AlexTrusk91
You should definately try problem sets. You never fully understand physics if you can't do the math (you might just have the illusion that you understand it).
I meet people all the time, who think that they understand a certain topic in physics, because they have developped a more or less accurate intuition, but they fail when confronted with having to calculate something and often fail as well with their intution. The ultimate test to whether or not you understand a certain topic in physics is always doing problem sets that involve math (and preferably understanding the derivations).
@@stauffap And can you help me abt problem sets like from where and how i should start to solve them like pre requisites and everything , i would really appreciate it
love this guys passion
An absolutely perfect lecturer
Whoever filmed this did a great job. Panning and framing. Spot on.
Would have been nice to see his laptop screen as direct instead of through the projector... still, a wonderful job as you said.
@@scowell wow wow, we're not talking about THAT much advanced technology here.
Fell asleep watching a ghost hunting video, woke up and this was on my TV thanks to autoplay. I didn't even feel groggy waking up because I was so alarmed by how good of a teacher this guy is. I'm more of a molecular biology person but I think I'll continue watching these!
I wish I took school more seriously as a kid so I could go to this school. This professor is amazing and I love his passion.
So do I.
Yeah, you can learn now.
I've seen a few other lectures from the other teachers and I didn't like them as much as these ones.
I think this is a gem, and we should appreciate we can watch the best of the best for free.
It's not limited to the 100 of the smartest hardworking kids anymore and it's awesome!
This is better though. All the learning with none of the crippling loans, egotistical teachers, or crushing deadlines! Einstein figured out SR while working as a patent clerk (though he did have a decent undergrad education)
You can always work harder now.
Teaching in MIT is like a superstar singing on stage. Everyone claps for the good performance.. Holy moly
People get excited when I stop speaking too, probably for a different reason
Six years ago, after I retired, I went through these lectures and the second semester with Dr. Zwiebach. Simply outstanding. I am back for a bit of review. Thanks Dr. Adams and Dr. Zwiebach.
;Touch and hold a clip to pin it. Unpinned clips will be deleted after 1 hour.😢hh
O❤
❤❤❤
Oh my goood, how can this be so much better than at my university?? The whole structure and order in which this is taught are just so clear!!
MIT is a very prestigious university. Very low acceptance rate because they take the cream of the crop in student's. If they do that for their students you can only imagine how they select their professors.
@@Ne012 yeah but : I went to Cambridge.. very selective on students.. terrible lecturing and teaching in general in the subject I studied which was economics.
They put him in camera for a reason. I imagine they have good and bad professors also
I wish I could get into MIT. These lectures have me hooked in a way I’ve never been hooked before. I’m trying my hardest to understand and I think I’m getting there
You’ll make it there! I wish you all the best! You deserve to be there.
I don't think that matters here. What he's saying doesn't apply to MIT.
A class that ends with an applause. That is how all classes should be.
I love the way the teacher brings those abstract postulates to live. In so doing he makes quantum mechanics crystal clear. He does it so well that one can not help feeling that there can't be a better way to put it (and I have thought about it several times). This work is invaluable! Just brilliant.
I love this so much. Trying to decide on Electrical Engineering or Physics. Did a long stint with the Marines and now using G.I. bill at a wonderful community college for freshman year. I have not been in school for a long time lol. MIT is still a dream and it feels SO good to be able to just listen. Watching these videos let's me know that I AM smart enough to sit here, even if life may not allow it right now. To be able to touch my mind to something I have wanted since I was a child is a gift and I wanted to say thank you to MIT and Prof Adams for doing this. One day, even if I am retired, I will take a degree at MIT , so stay awesome!!!!
i did bachelors in electrical engineering now i am going to switch to masters in physics!
How is it all going ?
I was the kid at school who said I wanted to be a Physicist when I grow up...
(... grow up.... something I might get round to one day ;-)
and got told, "there's no point we already know everything" by the _teacher_
I went on to do mechanical and computer engineering with Physics /QM as the stuff I do for fun.
but its more just a love of learning stuff
do what you enjoy
I have my class 11 English language exam tomorrow, and here I am at 10 pm learning about wave functions,(this lecture is amazing and addictive though).
Absolutely in awe at what Dr. Adams can do with just whiteboard and chalk. In another life perhaps I'd be in that classroom, or better yet in another world, following the Many Worlds interpretation of this beautiful subject.
9:32 When he realizes how long we've been working on quantum theory he looks like a father proud of his son's progress. If I weren't dedicated to applying physics in the more esoteric corners of computer engineering that moment alone would have pushed me into pure physics.
High school senior here, I'm actually fascinated with that EXACT field!
Great lecture. Can't wait for the free pizza at 5!
LMAO!!! xD
Dang. I missed it by 3 years...
The pizza is an imaginary component probably
@@NovaWarrior77 - I missed it by 4.
Wait it said free pizza at 5, not at 120…?
You are my favorite teacher. I watched these lectures for the first time about four years ago. Because of these lectures, I have a very good understanding of basic quantum mechanics. I just completed my post-graduation from IIT Guwahati recently. These lectures were very helpful during the last four years.
Truth be told, your IIT professors must learn pedagogy from these professors.
@itchy armpits I majored in physics.
Engineering Physics?
I'm never going to directly use any of this but that hasn't kept me from trying to just understand it for my own curiosity. Never know when something will appear at the edges of something else and come in handy.
This dude has come the closest so far to getting me there 🤣
your lecture is captivating, dear Allan! especially about superposition concept, i always just notice to math rule, but it has interesting physical meaning.
I wish there was a UA-cam channel with instructors who are obviously super interested in the topic they are teaching regardless of the subject
Man, I love this lecturer! He's so enthusiastic!
The teacher and course lecture is awesome, very professional. excellent job
These lectures were very helpful in turning my room into a physics laboratory as I attempt to re-create the Hitachi experiment using homebrewed CRTs. It was not, however, all that helpful in subsiding my extreme existential terror. I'm going to be seeing things that go through neither both holes, nor one of the holes, nor none of the holes in my nightmares now. Thanks a lot, guys.
Here, kid, have a cookie. :-)
I studied Telecommunications engineering. And now I realized that I was not that far to be studying formulas to be applied to Quantum mechanics. I mean, all these mathematical functions of waves are almost the same.
Of course it helps that I was reading and watching lots of videos about the "double slit experiment" and such, to know what are you talking about. But I never expected I would understand so much about Mathematics of the Quantum Mechanics.
It is all about Waves.... This concept of uncertainty (given by waves) is driving me crazy (in a good way)
This is the first Quantum Mechanics Lesson that I can "somehow" follow!
Thank You!! Amazing Professor!!!
Physicists always try to use the same math, it was the kind of math especially designed for them.
The concepts are easier to understand when you know the language, like psi and B*B
Prof.John Admis, I couldn't express my thanks for your awesome lecture. Wave fns / Fourier series and transform notes. Also you're ready to any questions. Thanks :) for all things
So thankful now of all the hard work I put into Fourier series and transforms and convolution that I can do these problem sets.
MIT is the only great source of quality education which is accessible to all.Thanks really i am greatly thankful to mit for giving the world a opportunity to become capable.
play ride of the Valkyrie when he asks for it, fits beautifully.
I liked the StrongBad reference at 40:02 :) very subtle.
It's amazing how accurate certain aspects of quantum mechanics can be calculated. They're basically just determining odds and they still get the right answer based on experiment. Weird.
Let me sound smart and say that is empirical knowledge 😌
11:54 "Happy electrons" this guy is the Bob Ross of Quantum
This is the one subject that still holds my attention.
Watching these for fun. What a great professor!
same. its completely irrelevant to my school work but its just so damn interesting
Watching before 1 day of exams
SOMMAN EDU did you pass? Are you now a quantum theorist
@@financewithsom485 how did they go
@@roku6194i am a software engineer now studied mechanical engineering that time this comment is 4 years back 😂
Really love the content available on youtube.
This is the best TV show I've ever watched
Thank you very much for such excellent demonstration!!
Came to his first lecture thanks to 3B1B, and here I am intending to go through as much as I can from Allan Adams ❣
In which video did he refer to allan?
20 years ago I had these same types of classes. No clue what was going on at the time. Now I get it. Maybe can go get that A I was looking for!
58:54 VERY slick teachable moment here. THIS shows that this guy knows his shit and gives a damn that the students can see how things connect.
You guys are too awesome. I finally start understanding quantum mechanics. I am a mathematician, chemist and aerospace engineer, but not a physicist. It is particularly hard to explain quantum mechanics to me, but you are outstanding. Will write my PhD thesis in quantum chemistry, which means that I can't have enough of quantum mechanics.
Ken, that's an odd statement. Obviously, in context, he is stating that a level of comprehension has personally been reached by him with enough confidence to state he is 'understanding' the current level of knowledge we hold. Obviously he isn't stating he's reached a mastery level of understanding that entirely exceeds that of all humankind to date... that would be a large assertion indeed.
Quantum chemistry sounds awesome!
Lies again? WTF WOF
Just what I need right now. Thank you!!
I paused the video and started Ride of the Valkyries for the III postulate. Definitely added something to it.
@1:00:12
Localized particles have less localized momentum because the momenta of the composite waves are cancelling and interfering with each other. Likewise, applying energy to the particles packet of waves causes the particle to move, albeit with some uncertain probability as to the direction/speed of movement. This movement reduces the coherence of the particle, and we become less certain as to where it is located. What is being described is the movement of a particle through space, but only if the particle is a secondary reaction created by the interfering waves.
Try to imagine the amount of waves (EM or otherwise) passing through us at any second. Now imagine these waves all form the standing particles that make us up. They are highly localized, and their individual momenta are uncertain. But when we apply a macro-force to the system, the momenta of all these particles becomes more certain, and they become less coherent in the static, localized positions they were in before. As the waves re-settle, they regroup, becoming coherent again with all the particles being reformed in a different place and once again, localized.
This guy is good! A lot better than any of the physics classes I took!
proved to be a major help in understanding the uncertainty principle : )
but how can you be sure?
Really cool lecture! I am from germany and go to University here, but your Profs seems really excited to teach and he makes fun jokes, its so easy to listen to him :)
I study at a Fachhochschule and yet I'm here watching these videos instead
What a great teacher
This course is just fantastic!!!
Dr. Benedict Gross from Harvard stated in his Abstract Algebra lectures that you could never know enough linear algebra.
Seems like the big point of the decomposition of wave functions into their linear combinations and superposition helps to illustrate both of their points.
Some favorites:
"Schrodinger's Cat, Wanted Dead And Alive"
"Heisenberg Might Have Slept Here."
And my own awful addition:
"Mathematicians consider it risque when infinities cancel. Physicists are more tolerant. They do not mind if it happens during energy jumps as long as it is discrete!"
Thumb this up if it is not completely horrible. My humor might have to be renormalized!
This is awesome!
Nachiketa Ramesh Here is one not directly related to quantum physics, but reasonably funny none the less:
"Entropy---It may not be the first bad law to keep a good man down but it is definitely the Second!"
CHistrue I didn't get this one. Second law of thermodynamics right? What man? How did it keep him down X(
Nachiketa Ramesh Well, you know, it ruins the perfect closed system. No perpetual motion machines. I guess if I have to explain it, the humor misses.
Should I try again?
CHistrue Yes please!!
The lecturer is fantastic.
Thanks Prof. Adams; absolutely brilliant intro into QM (not that I would know, I'm EE :-)). But just in case viewers need a perhaps equally well-taught lecture series on Fourier: There's an excellent treatment on this topic by Brad Osgood from Stanford available on YT. Highly recommendend!
great lecture series. thanks!
This was one of my professors at MIT a while back. The class was exremely hard. He was a genius of course. .
He talked pretty fast when teaching. . If for any reason you got behind , it was almost impossible to catch up.
Did you graduate?
One of the best Professors
1:17:00
I think the Geiger counter messed with the camera and microphone for a second based off the angle of that plate while you were reading it.
Cool!
I understand here in sir here till the 2019 and I had seen there 1 million subscription now it's 2.5 approx I'm quite happy
41:33 both sides of the equation are superposition in gravitational contraction
17:30 the moment i realized that he wrote his own name as a wave function! Hahaha
{X,P}= complete knowledge.
Postulate 1: Wave function.
Postulate 2: The wave function is a kind of 'generator function' of the probability that the particle actually be in certain x position.
26:30
Postulate 3: The states of the system are closed under linear combinations.
Mathematica package.
Fourier transform.
In his mind the epic depth of what he is teaching is the objective gospel. Flight of the Valkyries... Passionate dude.
Thank you all so very much.
Wow, they applauded for the guy. Well deserved.
Very great professor, very interesting way to teach
great lecture,,,
Exactly 40:00 - a very subtle homestar runner reference.
Please make more videos with Allen Adams! other Physics classes?
Are the recitation videos available? Thanks
The professor is amazing
amazing lecture
This lecture is love.
when the wavefunction is your signature
1:17:08 - I love how happy he is as he says "It's got uranium in it!"
I've never had a college professor that is so good at teaching they get applause at the end of a lecture...
At 9:30 he just realized how crazy this science is at what he is teaching and the enormous exponential Research and knowledge we gain and how fast we went from X to y in such a small space of time
I think he has add or ADHD cause I am the same when I look and notice what's Ian saying " I'am like dude whaooooo are your even realizing what you're saying"
There's something I don't understand: I've learned that quantum wave functions can be described as a "ket vector" in an abstract vector space called Hilbert space. The position wave function, for example, used to express the probability of finding the particle at a point, can be described as a vector in an infinite dimensional Hilbert space. But we also have the wave function used to describe spin ("spinor"), and this wave function exists in a 2-dimensional Hilbert space. So my question is, what is the relationship between these two different wave functions? I've also heard that the wave function contains everything that there is to know about the particle, but I'm like, "which wave function 😭😧?" I would be really thankful if someone could help!
The spatial wave function in the Schrodinger picture, psi, is not the same as a ket vector, | psi >. psi is the projection of |psi> onto the position basis:
psi = < x | psi >
| psi > holds all the information of the general quantum state and can be projected onto different basis's. That's why it's so useful. For example the momentum wave function can be arrived at by projecting | psi > onto the momentum basis:
psi = < p | psi >
But if you had just psi, the 'wave function', you still have a full picture of the quantum state because you can go to the ket | psi > from it.
@@paulryan94 Thank you for your answer, but the question I asked above was answered on physics stack exchange right after I made my comment. So it's no longer something that confuses me :). Here's the link to the question and answer on the site, if you're interested:
physics.stackexchange.com/questions/560132/wave-function-as-a-ket-vector-in-a-hilbert-space
Wow, a passionate physics lecturer :o
IMO, a "quantum vibrational wave/ripple" is set off at the point where the electron is fired. A quantum aerodynamics of sorts. The wave precedes the electron. It is this wave that is responsible for the distribution pattern as each electron, even though fired 1 at a time, is carried on it. It explains the "probability" of where each would land.
When you try to measure the electron, it is not the "conscious" act of doing it that causes the electrons to behave as particles, but it's because you break the wave. Thus, as there is no wave for the electron to ride on, it will come through the slit as an independent particle.
Thanks for the insight
When the Prof. rubs the chalk off the black board, doesn't it go into his open coffee bottle?
Chalk is nontoxic when consumed in moderation.
@@grandpaobvious Yes, may be Calcium in it is even beneficial for the bones!
if youre paying attention...the chalk is already in the coffee bottle, and also not in the coffee bottle
There is.probably a function to assess that
Love this series!
One question, why is the professor writing integrals like Int (the infinitesimal) (the function)?
Now that UA-cam provides an overlay graph of the most watched parts of the videos when you hover the mouse over the timeline, I find it pleasing that that graph has two peaks, a smaller peak at 6:25 and a larger peak at 36:37. Remind you of anything? =)
This man is so funny .
Creativity is intelligence having fun in motion right here .
Fun to go back and look at this 25 years after taking my first QM course. Having forgot basically almost all of it and seeing it again I honestly don't recall the magnificently simple interpretation of the position-momentum relationship from a Fourier perspective (obviously I don't do anything directly QM related these days). Very nice.
It's not an interpretation. It's a trivial mathematical lemma about certain types of linear operators on Hilbert spaces. It has absolutely nothing to do with quantum mechanics in the first place. Your WIFI router uses it for spectral shaping in at least some of the older protocols.
@@schmetterling4477 everything is contextual and without interpretation it has no practical meaning so it is most definitely an Interpretation. I’m glad it’s trivial, for you, but I’m not you For me I took this decades ago and haven’t used it since and don’t recall thinking of it this way. Most things are trivial in hindsight. I could say the same for someone marveling at being able to control a helicopter AFTER having gone through the process of experiencing it and learning it. It’s patently obvious what all the controls do. Trivial in concept. Why do you struggle with the execution? Why does anyone?
@@kevinwarren3998 If you have been taught an old style non-relativistic QM class, like I did, then it's highly likely that the professor would have done a very poor job explaining the actual physics of it. Ever since the Hilbert space representation of quantum mechanics was introduced by von Neumann, the teaching of this area of physics has degenerated into a hodgepodge of mathematical details that have little, if anything to do with the actual physics that underlies quantum mechanics.
This is a real pity because this way students do not learn enough actual physics to make sense of it all and they definitely don't learn enough mathematics to put it all into a larger structural picture.
This is what happens when several generations of teachers basically teach the material they have inherited from their own teachers blind, i.e. without asking the right physical questions about it. I don't think this is what von Neumann had in mind when he came up with the formalism, but it basically cemented "shut up and calculate" as the standard teaching method, even though the actual theory is much, much richer than that.
To put it into my context... it took me about 20 years to untangle it enough for myself to know where some of the educational pitfalls for the third semester student are (and I don't think I have found all of them, yet). As you said, in hindsight every one of the details that are being taught poorly or not at all are absolutely trivial. But to put them together and to develop the right intuition, that's a hard learning process.
@@schmetterling4477 Maybe next time when someone has an ah-ha moment, just let them enjoy it.
@@kevinwarren3998 I have been having ah-ha moments for the past 40 years between daily and weekly. There is plenty more where that came from. I am simply telling you that you haven't been taught well about quantum mechanics, that's all. If that upsets you, then welcome to the club. It has been upsetting me for well over three decades now.
Thanks this was really helpful for my grade 11th Quantum mechanics chapter 😀
I'm a little confused around 28 minutes or so (dealing with the probability when psi(x) is a simple sinusoid). If |psi(x)|^2 equals some constant value for all x, then the improper integral from negative infinity to infinity can't possibly be equal to 1, right? If the limit as x->infinity of the probability function doesn't equal zero, then the integral must diverge. Does this just mean that Psi(x) can't possibly be of the form e^ikx?
I 100% approve of the emphasis on dimensional analysis.
IVE SEEN YOUR COMMENTS ON QUORA, You’re awesome!!
@@charliecooper7458 Oh hey man, thank you. Let me make clear I am not a physicist. I'm actually an electrical engineer by training, and ever since graduate school 35 years ago I've just been really interested in physics and truly enjoy trying to help other people understand it. Alongside that, I have a few positions that aren't what you'd call "mainstream" (most re: consciousness), but I try to point those out if I mention them on Quora.
Thanks for the kind words - I hope you have a great weekend. Stay safe and well!
That was very intuitive
Wave functioning should be expressed on both sides of the equation.
I had quantum physics classes in 2018 taught by some brilliant nutter who couldn't teach a class to save his life... Smart but just terrible. What a great time it was
52:40
dont the cross terms have different signs because the norm squared is complex conjugate*function?
so we end up with
e^(i(b-a))+e^(i(a-b)), which is actually the sum of cosins? so we get cos(b-a)+cos(a-b)? so one might expect something that looks like big small small repeating?
What does it mean that the wave associated with a particle is the interference of many different waves? I mean what is the significance of each wave?
I think it means that the particle's wave can have any wavelength among those many waves with different probabilities. So it's nothing but the Uncertainty Principle.
great work
Welp that settles it, I definitely wanna be a physics major
No Name Sharma Really?
Yes! This was so cool :-)
+dubhad Physics major here - actually, there is a 1% unemployment amongst physics majors, unlike the 49% among business majors.
+Joseph Godoy that's probably because 99% of physics majors don't want a job.
+ahadicow No, quite the opposite. The 99% do have jobs, either in mathematics, physics, or sometimes on wall street or in business.
The details that I miss from quantum mechanical populist though it is inherent in all quantum mechanical equations is that; Kinetic energy of a quantum system is any where at different times while the potential energy of a quantum system is every where at the same time- this was demonstrated well through double slit experiment.
What goes wrong? I don't know and its good its not a physical configuration problem but an interpretation problem
I LOVE THIS GUY
At 59:53 - there need not be a wavelength for a momentum (unless we are presuming it a wave beforehand). E.g. A cyclist riding a bike has a momentum but no wavelength. Please clarify.
I was taking a calculus class and trying to figure a way to handle an integral of an infinite slope. I felt I had an explaination, and it turns out that my description was correct, though I did not know a technical definition, which turned out to be a kronical delta. To that end, the first stupid function descriped, it appears to me that it can be simply remapped through a manifold, more clearly straightening the function in away that multiple values are not taken. In that way, it reverts back to what I would call a kronical delta again, and there is once again a 1 to 1 function created, removing the stupidity. This is my opinion though. Anyone have thoughts or am I way off base?
@ timestamp 8:05, the proper pronunciation (of De Broglie) is DEE-BROY. Rhymes with LEE ROY.
this is very good online material