Deriving 1st Order Perturbation Theory (Energy and Wavefunction Corrections)
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- เผยแพร่เมื่อ 27 ส.ค. 2024
- Today I go through the derivation of 1st order, non-degenerate, time independent perturbation theory. I derive the general expressions for the first order correction to the energies and wave functions.
Bruh I’m not even a physics major, but i genuinely just like watching your videos
Osaid Sasi 😁
I'm not even a physics major (ME) and I still was able to understand everything you taught here. You have a real knack for teaching
Excadrill Excalibur thanks !
Don’t worry, even tho the views are low now, in about 4ish years, their about sky rockets from all the people on this channel coming back to watch this 😂
diddnt take 4 year lol
lol here i am 4 years later
reporting after 5 years o7
I really don't enjoy General Physics II. I hate circuits with a living passion, and this class is just a reinforcement for not doing Engineering. I really love theory, and watching stuff like this, even though I don't understand it fully, really motivates me to continue through, because it's of what's to come, so I can push through to get the theory. It's what motivates me to not switch to a math major to get my theory fix lol.
Also a video idea: The derivation of the Euler-Lagrange Equation.
Hahah I'm completely the opposite... I hate theory and love circuits. Which is why I chose electrical engineering.
CrosisBH engineering is not similar to physics II, but I get what you mean. Exploring the obscure...
This is actually a method for solving nonlinear differential equations. Nonlinear differential equations dominate a majority of applied math. Doesn't have to be engineering or physics, it can be chemistry and biology as well that have nonlinear equations solved using perturbation methods.
Dang, i first watched this video a year ago and i thight you were writing in some ancient language. Now i am being able to fully understand 1st order, 2nd order, non-degenerate and generate pertubation. I am for the first time in my life proud of myself. Lmao😂
I have absolutely no idea what you are talking about, but I love it.
Can't wait to be able to understand this lol
Entering undergrad physics next year at Purdue!
Love the channel!
Same.
Doing undergrad chem next year and Quantum mechanics is in our syllabus
Unfortunately, you're probably gonna have to wait about two-three years until you get to this.
@@bobross5716 you're probably right... Still excited though
I'm starting in the fall as well!
@ThePoptard I'm curious; can you share your GPA and SAT score? I'm really interested in going to Purdue.
Do a video on Taylor Series and how it's used in physics.
I read this as Taylor Swift and now I want to see a video on that instead
sin(x)=x boi
sin x = x - 1/6(x^3) + 1/120(x^5) + ...
🧐
@@danielsykes4251 Well you might as well finish the rest of it if you're going to go that far lol
I’ll leave that as an exercise for the reader.
As a science-enthused junior in HS taking AP physics 1 these videos are amazing! I hope to keep watching and understanding more and more as I progress in my education.
Bro, I'm a Law student with no physic related background, had no experience learning them (didn't took them in school), have no idea what it was until I stumbled upon your channel.
Needless to say, I'm hooked and look foward to every video you make and tbh, you make it fun and interesting for me 😊
@@hamzaa.8082 it's okay. I can defend myself 😀
I started following for the funny videos, but this is saving me right now!
Fine video. Some suggestions for future lectures are:
-Solving the hydrogen atom problem with Schrodinger's equation
-Quantum mechanics in crystalline materials (e.g. bloch theorem)
-Tunneling (deriving electron current through barrier)
"Today I'm assuming you need help with your quantum homework" YUP
Non-degenerate? Impossible I watch anime.
This is Sweet! I had a perturbation class last semester, and my final project was using it for the hydrogen and helium orbitals
Oh that sounds awesome!
Physics explained by an escaped convict 😋
Nice observation.
@@doctorlazarus8854 if I didn't observe it, it wouldn't exist. 😁
my QM homework has been saved! it is now 5 days late instead of 7! Thank you!!!
Hey just a little teaching advice/compliments from a person who studies education:
1)obviously you catch yourself standing in front of derivations, which is good!
2) Avoid using phases like, "That would be stupid" or "I made a stupid mistake". When teaching students, using that language can often turn off those who are learning the subject and can become conditioned to think that making mistakes or assuming the wrong thing (perhaps by accident, idk) means that they themselves are not smart enough for the subject. Instead, try using phases like, "I made a mistake! Good, now I know how that goes", or "That would not be a productive idea due to..." Vernacular matters with those who are learning something new as it can affect how well students feel about themselves with the subject; hence affecting their overall performance.
3) You're are very clear when describing complex processes! Perturbation theory is extremely complex and is not often explained well. You really know your stuff! Keep making these videos!
-From a former Math major.
Great video as always. Needed a review if this stuff for a project I'm working on and thus was perfect years after being made. Good luck with the disertation, Andrew!
You know.....as a geophysicist I consider myself a physicist....but holy hell you killed me in the first minute.
In undergrad quantum mechanics right now, just finished the hydrogen atom energy states and eigenfunctions now moving on to perturbation! This video really helped my understanding thank you for making it
Thank you for calling us smart in your intros 🥺
Aww this brings up some memories. I had an excelent quantum mechanics prof. You remind me of him haha
It's nice to see this type of content in youtube
Really good video nice and condesed perfect for revising if you are not to familiar with the matter anymore :)
Thanks a lot and greetings from TUM in Munich :)
Thanks a lot!
My friend is just an engineer and he was able to get the first half. Amazing.
Was just about to read this chapter in Griffiths and take notes to that. Thanks for the free lecture and a better explanation 😍😍
brooo i just took a course on dynamics and chaos and perturbation was a part of it. stoked to watch this
I have no idea why I’m watching your videos. Hell, I’m not even really interested in Physics; I hope to major in Psychology when I graduate high school. Perhaps I just enjoy watching someone who is passionate about their field. Keep doing what you do.
I remember there being an awesome series of lectures from maybe Washington Uni on perturbation theory? The lecturer was SO good
i was just looking up on this in Principles of Quantum Mechanics by Shankar. They do it in a slightly different way, but i think your method is easier for me to understand. Thanks man!
I took Quantum a year ago, alas a little late to have fully benefited from your video. But thank you Andrew for posting this. You're doing good work.
Wish this lecture came about two weeks ago before my test 😒🤦 Anyway it's never too late to learn! Thank you!
Really well presented video! I’ll be studying functional analysis next year so I can finally see how these inner products work in Hilbert spaces..
Thanks! You have to be careful when talking about vectors in a hilbert space from a QM context because initially it was only defined for discrete vectors. When you generalize to continuous ones (like position or momentum eigenstates), there's some additional criteria that has to be satisfied which is kind of interesting. Hence why your dot product becomes an integral over a continuous index.
Andrew Dotson where the views at 😩 please don’t give up on this style of video!!
Hello! May be you could make a video about deriving diagram technique for some interaction (I mean using wicks theorem and s matrix) ? Honestly, I am more interested in QED, but I think it is hard and tidies enough to put it on the channel. Or may be you could cover some general topics from QFT , there are many interesting theorems and ideas !
Generally love your channel , you are great! Keep doing that !
It helped me a lot in understanding the theory
Love this, would like to see more! I'm taking my second QM class next year and this lets me see some of the stuff i can look forward to :)
Andrew, could you do a video on functional derivatives? Thanks!
Andrew Dotson you the boss.thanks man
just reviewing for an exam thanks Andrew
12:55 LOL that totally caught me off guard. "That be stupid!" hahahahah!
I am taking a module on Atomic physics this semester and am finding it really hard to get my head around perturbation theory especially the linear algebra as I have tried to avoid it so far! This has helped me get a slightly better grasp of what's going on though! Thanks
More please! Also would like a video to about if perturbative theory converges
Yup, you are doing it correctly - From a computer science major
😂😂😂
Nah I’m just a 15 year old aspiring Astrophysicist, I kind of had know Idea what’s going on! I can understand stuff conceptually but I’m just in like a lower level physics class! Really excited to understand this video
This derivation, or one equivalent, was on my quantum exam last semester, just deriving the first order correction to the energy
This was an adventure
Thanks Andrew!
epic video thanks very much vv clear notation !
Do videoes on one dimensionel harmonic oscilator problem of schrodinger equation
Amazing video as always, actually very helpful as we don't do perturbation theory until third year at Cambridge unfortunately :'(
Great job bro,im a fan
Is there a proof you can independently impose the condition = 1? Cuz I’m not convinced that you can impose that and | E> = |E_0> + \lambda |E_1 > + … .
Do you plan on continuing the PhVlog series? NGL you inspired me to start my own when I finish my masters next year and (hopefully) move on to a PhD
I love these physics symbols
hey, nice video, thanks for sharing! I am thinking about conditions of expanding in known basis... Let's say I have any known basis (as here) I can imagine any creazy operator I want, is that I should be always able to express its states in terms of known basis? assuming that there is some transformation that links my old operator that eigenvectors I know with my "new-creazy-any I want" operator. But if such transformation doesn't exist my old basis is useless, right? So that's why we assume here perturbation is small, to be always able to assume that full Hamiltonian is like "little" transformed from unperturbed (transformed I mean, any infinitesimal perturbation can be a rotation that can be unitary operator) Does it make any sens? Maybe I totally confused all things,
cheers
Thanks you do much! Amazing how hard textbooks fuck up this chapter...
Why am I watching this when I still haven't even started physics yet
Entering Stony Brook for physics can't wait to learn all this.
I remember doing the 2nd order with the help of Landau textbook!
Hey Andrew. Can you make a video on the black hole announcement. Thank you
Basis transformation
|E_n> = |E_n>
|E_n> = I |E_n>
= ∑ₘ|Eₙ>
|Eₙ> = ∑ₘ|Eₘ>
I hope i intuitively understood this concept, so basically you are saying, that by approximating our wave equation with a series of a known and solvable wave equation/s which will eventually with adding terms converge to our unknown wave equation and give us the best approximation of the end result? Then would our results come out as: this wave equation is like that one, but with this corrections which converge to our unknown but now a bit known wave equation, which is accurate on some decimal places? Thank you!
Next video on Taylor series and its uses please.
I find it halrious that half of notations we use are different, but we all know F=ma is same as D=AB. Was cool video though
Make a video about the black hole image, gotta get in on that hype!
I heard somewhere someone first proved it never converges, it'll go close but never converge
Can you upload a PDF of your notes that you teach during every video in the video details??
Is this related to time independent density functional perturbation theory?
What are the dimensions of your whiteboard? Have been thinking of getting one as well when I get into college.
I'm going to need a lot more math, in my math very soon if I want to do physics
This notation makes me cry
This. Is. LIT dad.
where is the video tutorial on convergence of perturbation series?
Can you please do a video on mathematical prerequisite for self studying general relativity?
11:54
Ah yes, the infamous left-hand rule. Thought you could sneak it in there but we all know what you were trying to go for.
Love it
I am finishing up an MSc Physics course.. I took the QM exam, I think I failed it. I still don't get any/much of this.. :(
FLAMMABLE👏🏻 MATHS 👏🏻COLLAB👏🏻
Where’d you get the white board?
Thhhhhhaaaaank u very very much
When will you be adding English subtitles?
At first glance, I thought he was expressing the eigenvalues of the Hamiltonian as a ket.
Why don't you include the I=j=1 term in the labmda expansion?
dhvsheabdh you don’t include the i=j=1 term because that gives you a lambda squared term which we are discarding because we are doing a first order correction!
@@TheNiTeMaR3 I thought of that during, but then I thought I disagreed that that would do it.
Andrew make a video on perturbation theory 2
Do some example pls
absolutely more orders!!
Nice watch
0:09 aka the simplest kind of all the PT
board usage could use some work, maybe consider getting a second?
nice video otherwise, thanks for the refresher!
Why don’t u write the wave function as Psi??
psi(x) is the inner product between the x-basis vector and the abstract ket vector |psi>. So psi(x) = . I'm just keeping it as a vector
@@AndrewDotsonvideos
Int zetli text book they use
Psi and phi
(I posted this on another video as well) Hey Andrew, considering you're in NM you should consider coming up to visit Los Alamos in the summer, if you're around. There is really no other way to directly contact you since you don't have any email or other contact information posted in your descriptions, so here is my invitation.
Best,
Eb
eb f to the national lab ?
@@AndrewDotsonvideos Yeah! Come by and visit for day? You could vlog about it, after leaving lab property(no photos). You can grab a drink after with a few of the 1500 interns.
@@AndrewDotsonvideos join students@LANL on Facebook and I'll confirm you.
Nice! And first
hey what uni are ya in im a mcgill in the honourds physics
Patrick Guest im at UBC! UBC used to be a part of McGill lol
I thought this was an english speaking channel ?
I'm here, french, in first year of Earth Sciences, understanding nothing, having less electricity in my brain than in wood.
16:33 is that a southpark reference?
Yes😂
@@AndrewDotsonvideoslol subtle. By the way I approved quantum mechanics II and got my astrophysics degree since I left that comment. Thanks for making these videos 4 free. Respect🤙
I just watched a 23 minute video and haveee no idea wtf just happened. Im just tryna get fluid dynamics down for the MCAT fam
Also Dotty ,if potential is very complicated , all these methods are freaking tedious!!!!!!!!!!!!!!!
Can you make more of these white board type of videos, but with calc 1 topics
I'm here :D
Please be my future prof