Unpacking the Schrödinger Equation

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Professor Dave Explains

Professor Dave Explains

3 жыл бұрын

We've talked about the Schrödinger equation before, but we really didn't dig into it with any depth at all. Now it's time to really get in there and do the math. What is the Hamiltonian operator? What is the time-independent Schrödinger equation? What we can we do with this equation? Let's find out!
Script by Hèctor Mas
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Пікірлер: 149
@Fourfingerssixtoes
@Fourfingerssixtoes 3 жыл бұрын
Think I'll get back to my trigonometry and polynomial division for now. I'll see you guys in about 50 years
@nabzim
@nabzim 3 жыл бұрын
Polynomial division is more painful to me than this.
@jokerman9295
@jokerman9295 2 жыл бұрын
Lol. If you are thinking about doing physics in university, just remember it only gets harder as time goes on.
@andym.s.5231
@andym.s.5231 Жыл бұрын
@@jokerman9295 My entire "Physical Chemistry" syllabus can be condensed to pretty much 100% of all the videos in this playlist. It feels like they just took modern phys and replaced the label with fancy chemistry for those in chem programs. srsly... I didn't go for a degree in physics for a reason, yet here I am. send help
@jokerman9295
@jokerman9295 Жыл бұрын
@@andym.s.5231 Well it depends on what your teachers have you doing and how strict the tests are. If theres a lot of problem solving then just practice, no other way around it. Usually that's the best way to actually learn the science as well, instead of just passing for the degree. I'm doing computational physics right now which is such a broad and useful field, you can study pretty much any topic computationally rather than experimentally and develop coding skills.
@lordspongebobofhousesquare1616
@lordspongebobofhousesquare1616 3 жыл бұрын
Hi professor Dave, just wanna drop in and say thank you. I watched your tutorials to cram for my university joint entrance exam. I don't have the money for tutoring, but I managed to collect enough money to rent a home wifi so I can watch your videos among other things. Your videos are very concise, which I like. I managed to get accepted (to study mathematics) and your videos played a huge role in making that happen.
@thegermanempire9015
@thegermanempire9015 2 жыл бұрын
Great job man. Hope you’re doing well.
@matthewrussell7069
@matthewrussell7069 3 жыл бұрын
Still remember my prof teaching this 15 years ago. The colored fonts are incredibly helpful!
@highwaymen1237
@highwaymen1237 3 жыл бұрын
Good point. Richard Feynman visualized parts of equations in different colors.
@higgs_boson2231
@higgs_boson2231 3 жыл бұрын
I love how you are one of the few people on yt to get fully in depth into QM in a way in which we can understand. You deserve a larger following!
@adleneboulebtateche156
@adleneboulebtateche156 3 жыл бұрын
Professor Dave really knows a lot about the science stuff. impressive !
@kazumasatou5600
@kazumasatou5600 3 жыл бұрын
Thanks for this video, professor. Too many people are far too intimidated by the math behind quantum mechanics, though I'd argued it's undoubtedly the most beautiful aspect of this theory. We definitely need more science communicators.
@davidpage8580
@davidpage8580 3 жыл бұрын
I've been following this series as an amateur. I understand very little but Professor Dave's talent for explanation still allowed me to gain some mild insight into the topic. Thank you
@adamdrewko233
@adamdrewko233 3 жыл бұрын
This is so... enlightening! Thank you so much for this series and the whole of your work.
@ultradripstinct7105
@ultradripstinct7105 3 жыл бұрын
I've gained 40 brain cells by watching this
@tsekwongtai9005
@tsekwongtai9005 3 жыл бұрын
I've got much a lot!
@birdsayshello
@birdsayshello 3 жыл бұрын
ive lost brain cells truing to understand lmao
@Ihab.A
@Ihab.A 2 жыл бұрын
Prof, I started giving thumbs up to your videos before I even see them! Those are invaluable treasures! Grazie!
@akshatpandey9141
@akshatpandey9141 2 жыл бұрын
I recommend ur channel with my friends. They loved it. Ur explanation is superb.
@tommasoprocida4348
@tommasoprocida4348 Жыл бұрын
Thank you for this video man. Studying Quantum at the moment but struggling to follow the narrative so to speak of some parts. This was really well explained and helpful!!!
@MrBananabomber123
@MrBananabomber123 3 жыл бұрын
Thanks for making these, I am very excited for the next one!
@aerofiles5044
@aerofiles5044 3 жыл бұрын
i love this channel so damn much
@cliffordwilliams9597
@cliffordwilliams9597 3 жыл бұрын
YAY Thank you !! I've always wanted the Schrodinger equation fleshed out for me !!!
@smlanka4u
@smlanka4u 8 ай бұрын
A very profound explanation. Thank you so much Prof. Dave.
@swipe7249
@swipe7249 3 жыл бұрын
Dude, I just had a class on this today. Didn't make any sense so thanks for this.
@brianrasmussen1711
@brianrasmussen1711 3 жыл бұрын
I’m in quantum mechanics right now and this is extremely helpful.
@carson8074
@carson8074 3 жыл бұрын
Woaw, this is really helpful! Thank you prof Dave!
@ruchirrawat8804
@ruchirrawat8804 3 жыл бұрын
i'm grateful to have learnt so many quantum mechanics concepts and beautiful derivations in high school itself. thank you so much u r indeed one of the best teachers on youtube. : )
@asdfghjkllkjhgfdsa9161
@asdfghjkllkjhgfdsa9161 3 жыл бұрын
Whoa! Way over my head. Ill be back after watching a few other videos so this makes more sense, i promise!
@lowkey_entertaining9723
@lowkey_entertaining9723 3 жыл бұрын
I have never needed to pause a video so much in my life
@roxannengmingli2697
@roxannengmingli2697 3 жыл бұрын
reconsidering my path in sciences
@parthapaul4306
@parthapaul4306 3 жыл бұрын
very happy to see someone is making useful content
@gnikkings
@gnikkings Жыл бұрын
You should be proud, this is the best QM content on KZfaq.
@0cgw
@0cgw 3 жыл бұрын
A nice way to think about the Schrödinger equation is to take Ψ=exp ( iS(𝐱,t)/ℏ+o(1)) and substitute it into the Hamilton-Jacobi equation: H(𝐱,𝛁S,t)=-∂S/∂t in the limit as ℏ→0. So for a non-relativistic particle in a potential V(𝐱) we have H(𝐱,𝛁S,t)=(𝛁S)²/2m+V(𝐱) and -iℏ𝛁Ψ = Ψ𝛁S+o(ℏ), so that -ℏ²𝛁²Ψ = [(𝛁S)² -iℏΨ𝛁²S+o(ℏ²)] Ψ, and -iℏ∂Ψ/∂t = Ψ[∂S/∂t+o(ℏ)]. Hence, neglecting terms which are o(ℏ) we have the leading order equation: -ℏ²𝛁²Ψ/2m+V(𝐱)Ψ=iℏ∂Ψ/∂t, i.e., the Schrödinger equation. This is related to the path integral approach, where exp ( iS(𝐱,t)/ℏ) occurs in the path integral.
@1imag337
@1imag337 6 ай бұрын
thank you😊
@Vishnu-jr3wv
@Vishnu-jr3wv 5 ай бұрын
I didn't understood 🥲
@cedricsipakam2601
@cedricsipakam2601 2 жыл бұрын
You explain verry well professor Dave. Love your videos.
@wwmheat
@wwmheat 2 жыл бұрын
Thank you professor Dave, great explanation, as well as all the others! I have a question though. On 5:08, for derivation of time-independent equation, you assume that psi can be represented as phi(x)*ksi(t), but how can we be sure that this is the case? I mean, isn't this trick only legal if our function is separable? If so, what is the justification for the fact psi is separable? Thanks
@salaheddinesb7312
@salaheddinesb7312 3 жыл бұрын
Damn . This what I am looking for! Please explain the rest! Thank you very much!
@angelosevilleno2851
@angelosevilleno2851 3 жыл бұрын
Extremely nice lecture on QM!
@hi7814
@hi7814 Жыл бұрын
I am gratefull to find this KZfaq channel
@schifoso
@schifoso 3 жыл бұрын
That dam reminds me of the Vajont damn at Longarone. Great breakdown of the equation as well as an excellent explanation of what the terms mean.
@pederjohnson4574
@pederjohnson4574 7 ай бұрын
8:33-10:23 why is there no +C term when integrating? Does the arbitrary constant for the left side somehow equal to the right side and they cancel out?
@chimetimepaprika
@chimetimepaprika 3 жыл бұрын
Heeeell yeah! Do you have one on Dirac Equation? This is tight!
@brianthibodeau2960
@brianthibodeau2960 2 жыл бұрын
Hey Prof Dave! Just wana say I love your videos. I have a comment- you say that we have just shown the time dependent part will always look like that but I think you should add that it will look like that under the assumption of separation of variables, where the the spaciotemporal evolution is uncoupled. This could be true sometimes and is possible but is not generally or always true.
@nicholascamatti3162
@nicholascamatti3162 2 жыл бұрын
At 7:10 when you divide both sides by phi(x)*csi(t), why did it cancel out with the terms being acted by the potential operator? Is this a rule for operators?
@TheSunsen1
@TheSunsen1 3 жыл бұрын
IVE GONE THROUGH 3 PLAYLISTS. AND STILL HAVNT FOUND IT. Still learns some interesting things
@tune_m
@tune_m 3 жыл бұрын
Very clear, thanks!
@lilydog1000
@lilydog1000 3 жыл бұрын
Excellent tutorial.
@leventegyorgydeak1300
@leventegyorgydeak1300 4 ай бұрын
In the beggining the premise was that psi is seperable into a product of two functions such that one only depends on time and one only depends on space. Given that all of the conclusions in this video only apply for seperable solutions right? Or is there a law that says all solutions of the schrödingen equations must be seperable?
@ganishk3568
@ganishk3568 3 жыл бұрын
During 7:25 how did you concelled the variables in Potential energy operator since they also operated by the Potential energy operator we don't know any information about it, then in what aspect is it right? Please explain.
@0cgw
@0cgw 3 жыл бұрын
That was an error, really he should have treated it in the same way as the kinetic energy term. In general, you cannot cancel off the argument of an operator. However, IF V is only a function of x, which is common, then in the configuration space representation (where x^ acts by multiplication by x, and p^ acts as -iℏ∂/∂x) then V^ acts by multiplication by the scalar V(x), and the calculation is okay. There are a few minor errors in the video, such as a missing constant of integration etc. when deriving the time dependence, though this can be absorbed into a redefinition of the spatial wavefunction.
@nalunaroco978
@nalunaroco978 3 жыл бұрын
YOU SAVED MY DAY
@ayman7209
@ayman7209 3 жыл бұрын
Thank you Dave
@jennykim9159
@jennykim9159 Жыл бұрын
omg I cannot thank you enough😭 thank you soooo much!
@D1stop1an
@D1stop1an 3 жыл бұрын
Can you debunk the Michelson-morley test? I've been seeing this one creationist trying to peddle this on his channel
@designtechdk
@designtechdk 3 жыл бұрын
When dividing by phi(x)xi(t) you implicitely assumed that the potential energy operator results in a function V(x,t) multiplied by psi(x)xi(t) instead of being a differential operator or something :)
@humanbeing9731
@humanbeing9731 2 жыл бұрын
Awesome & smooth
@jonocour
@jonocour 3 жыл бұрын
at about 10:13 mark, why when doing the integration with out any limits is there no constant added on to the end.
@gautamramasamy2482
@gautamramasamy2482 2 жыл бұрын
I think he skipped steps to make it less complicated. I believe the constant of integration works out to be zero
@vanillabean7832
@vanillabean7832 2 жыл бұрын
Extremely helpful
@mayankdas9742
@mayankdas9742 9 ай бұрын
You are doing god's work my man. Thank you so much.
@Letsfeelthenaturee
@Letsfeelthenaturee 3 жыл бұрын
You are really very brilliant, sir. Hope you will be more and more helpful........
@Letsfeelthenaturee
@Letsfeelthenaturee 3 жыл бұрын
yeah.......
@jamesmark8679
@jamesmark8679 3 жыл бұрын
Hi professor can you do schrödinger equation for a 3d particle please....thank you
@henryrroland
@henryrroland 3 жыл бұрын
I want moooore. I need more
@tungvuthanh5537
@tungvuthanh5537 3 жыл бұрын
this help me a lot in reading and understanding "Quantum Computation and Quantum Information" of Michael nielsen and Isaac chuang
@kiiometric
@kiiometric 3 жыл бұрын
7:00 Why does the operator V lose the phi and xi? Does it not have partial derivatives in it?
@jonocour
@jonocour 3 жыл бұрын
the operator V is not got any partial derivatives and is just multiplies by the wave function, the position and time functions. So when dividing by that, they both cancel and goes to 1. So only the operator of V remains
@deeprecce9852
@deeprecce9852 3 жыл бұрын
Hahaha..i think it was at least over 10 lectures on this equations alone..now its summarized in a few short videos, enjoyed it all physics fans👍👏❤
@NovaWarrior77
@NovaWarrior77 2 жыл бұрын
SO CLEAR.
@ARBB1
@ARBB1 3 жыл бұрын
Interesting note is that one of the proofs the Sch eq is non-relativistic is because the functions can be separated in time and space sets of solutions as you did in the separation of variables.
@johnmcclelland649
@johnmcclelland649 3 жыл бұрын
Dave, just dropped in on your channel after a short absence. This presentation has provided a superb explanation of some challenging (for me at least) maths/physics, as per usual. It occurred to me, however, that very few flat earthers seem to have made it to these videos. I haven’t yet seen anyone comment “we see too far” or “moonlight is cold” or “water finds its level” in the comments section, throughout the series. Are you concerned that your videos are missing that market? 👍
@johnmcclelland649
@johnmcclelland649 3 жыл бұрын
Ooooh, Grape, just trying for a bit of lightheartedness, man. Cool your jets!
@FGj-xj7rd
@FGj-xj7rd 3 жыл бұрын
There was a short clip of water in fhe video. Some flat earthers will say "Water finds its level"
@johnmcclelland649
@johnmcclelland649 3 жыл бұрын
Flavio Gjoni yes, exactly! Totally disproves the globe......? I was making (trying to make) a joke and it appears I’ve been shot down in flames by a ???troll ???flatearth scout
@FGj-xj7rd
@FGj-xj7rd 3 жыл бұрын
@@johnmcclelland649 Not me lol
@johnmcclelland649
@johnmcclelland649 3 жыл бұрын
Flavio Gjoni I know! It was GrapeSkoda.
@Bangy
@Bangy 3 жыл бұрын
Just finished physics exam. Guess I won’t need to know this anymore
@OMaMaRMY
@OMaMaRMY 3 жыл бұрын
Sees thumbnail: Aight imma head out
@cuteworld4984
@cuteworld4984 3 жыл бұрын
Hi teacher I used your Chanel everyday. Cause I just wanna be like you 🤩🤩🤩🤩🤩 I’m from Chile 🇨🇱
@kimitsudesu
@kimitsudesu 3 жыл бұрын
Why is it valid to separate psy into phi and ksi? You wouldn't be able to do that for most functions.
@lilydog1000
@lilydog1000 3 жыл бұрын
To separate the (x,t) function into configuration space variable only, and time variable only.
@constpegasus
@constpegasus 3 жыл бұрын
Awesome.
@ashutoshjha225
@ashutoshjha225 3 жыл бұрын
This is a great brain exercise
@dns911
@dns911 3 жыл бұрын
Clean and crispy
@skat3r430
@skat3r430 3 жыл бұрын
Oh my god! I swear the book just threw the equation at me and said it wasn’t derivable! I finally get it!
@adityabhatt8549
@adityabhatt8549 Ай бұрын
thank u for saving me boss
@Octoberman07
@Octoberman07 4 ай бұрын
When i hear your Vibing intro i forget all my tension it looks like i'm watching cartoon😊
@jjwrenmusic
@jjwrenmusic 3 жыл бұрын
Why the hell did I click this video thinking I might have the tiniest clue of what Dave is talking about?
@yahya8578
@yahya8578 3 жыл бұрын
Waiting if he gets to 1 Million
@bigbrothersinnerparty297
@bigbrothersinnerparty297 3 жыл бұрын
Did this get reuploaded?
@ProfessorDaveExplains
@ProfessorDaveExplains 3 жыл бұрын
yeah, i made a really stupid error and someone caught it so i decided it was early enough to just print again
@Jehannum2000
@Jehannum2000 3 жыл бұрын
@@ProfessorDaveExplains Was it just the delta symbols?
@ProfessorDaveExplains
@ProfessorDaveExplains 3 жыл бұрын
yeah, so dumb of me!
@Letsfeelthenaturee
@Letsfeelthenaturee 3 жыл бұрын
@@ProfessorDaveExplains but amazing......🍏
@gnikkings
@gnikkings Жыл бұрын
12:27 I don't know why this is so satisfying
@amyfyzee9894
@amyfyzee9894 3 жыл бұрын
HEY CAN U MAKE PRACTICE PROBLEMS IN MATHS PLZZZZ.
@utkarshraj3272
@utkarshraj3272 8 ай бұрын
👏
@sublimechalicefpv7714
@sublimechalicefpv7714 3 жыл бұрын
I wish I understood what Prof Dave is saying???
@michaelgonzalez9058
@michaelgonzalez9058 Жыл бұрын
Time is done by the time machine in London's museam
@swl1987
@swl1987 2 жыл бұрын
Professor Dave seems like such a nice guy until you watch one of his debunking videos. The jingle lyrics for the debunking videos should be, "Don't fuck around with Professor Dave - he don't take your crap." Thanks for the videos! Learning lots.
@kelton1920
@kelton1920 3 жыл бұрын
I’m 11 years old but some how I understand this! Also, Dave, you are the best KZfaq teacher EVER (I said you are instead of you’re because you deserve more words(and subscribers!))
@kelton1920
@kelton1920 3 жыл бұрын
Also I have a KZfaq channel called NerdyNinja education
@Gremriel
@Gremriel 3 жыл бұрын
I think I understood some of the words.
@MisterItchy
@MisterItchy 3 жыл бұрын
Whatever you do, don't be all cocky after watching SciMan Dan's physics lesson and then click on this. It doesn't end well! I went from "psh, that's just common sense" to "wudafuq is all this?" in about 3 seconds.
@richardaitkenhead
@richardaitkenhead 3 жыл бұрын
Love the new haircut
@miguellara2289
@miguellara2289 3 жыл бұрын
What's important is,Will it make a good t shirt quote?
@eyoelgashaw5089
@eyoelgashaw5089 3 жыл бұрын
Why don't you just make a playlist on differential equations and all this quantum mechanics chapters.
@ProfessorDaveExplains
@ProfessorDaveExplains 3 жыл бұрын
quantum mechanics goes in the modern physics playlist. i will eventually do differential equations and that will go in the mathematics playlist.
@eyoelgashaw5089
@eyoelgashaw5089 3 жыл бұрын
@@ProfessorDaveExplains ohh thanks professor Dave. what about this video? which playlist does it goes in?
@ProfessorDaveExplains
@ProfessorDaveExplains 3 жыл бұрын
modern physics
@PastaTurtle
@PastaTurtle 3 жыл бұрын
Hi
@overlordprincekhan
@overlordprincekhan 2 жыл бұрын
U explained shit that my professor couldn't done in the last 4 lectures
@AliHassan-fr9kx
@AliHassan-fr9kx 3 жыл бұрын
I want episodes about electronics
@ProfessorDaveExplains
@ProfessorDaveExplains 3 жыл бұрын
i'll do electrical engineering and computer science at some point, probably next year
@jackerty
@jackerty 3 жыл бұрын
I think you have logical error in the video. Assuming phi's variables can be separated doesn't lead to conclusion that time-independent Schrödinger equation is enough to know time-evolution of the system as you haven't checked if variables can't be separated. Now, what I gathered from the internet separability is fine long as potential energy isn't time dependent. en.wikipedia.org/wiki/Schr%C3%B6dinger_equation#Time-independent
@pqrstzxerty1296
@pqrstzxerty1296 3 жыл бұрын
What happened to his cat ?
@harryshepherd4232
@harryshepherd4232 3 жыл бұрын
First. Therefore, sexiest.
@user-pk9qo1gd6r
@user-pk9qo1gd6r 3 жыл бұрын
Reminds me of the time when I though having good grades and being first in my classroom was enough to suceed at life. Well look at me now... kids can really be dumb.
@tsvetanstoychev655
@tsvetanstoychev655 3 жыл бұрын
Good at the sex, tho?
@harryshepherd4232
@harryshepherd4232 3 жыл бұрын
@@tsvetanstoychev655 Oh, God, no. Awful.
@frankchen4229
@frankchen4229 3 жыл бұрын
The earth is flat AND round at the same time
@ProfessorDaveExplains
@ProfessorDaveExplains 3 жыл бұрын
You're a little lost, kiddo.
@albertmockel6245
@albertmockel6245 3 жыл бұрын
@@ProfessorDaveExplains earth = cat
@frankchen4229
@frankchen4229 3 жыл бұрын
@@ProfessorDaveExplains im just messing around lmao
@ski.7
@ski.7 3 жыл бұрын
I'm starting prof. Dave syndicate (A team that supports sir's channel to grow by sharing or etc (if we can't support on patron let's support in this way) :) ) let's make a discord channel or insta page to make sir more famous and share knowledge #prof.davesyndicate like this comment if you agree
@eXcalibre_
@eXcalibre_ 3 жыл бұрын
Is this the world’s hardest equation?
@skat3r430
@skat3r430 3 жыл бұрын
One of them yes
@Mkultra-235
@Mkultra-235 10 ай бұрын
Probably not I was able to follow mathematically as a high school student. But I really really wanted to understand this because of Nuclear physics. Piece by piece it will make more sense keep trying
@andrewe6839
@andrewe6839 11 ай бұрын
yuh yeah yuh yeah yuh yeah
@sollinw
@sollinw 2 жыл бұрын
OMG🤩
@timtarbet4594
@timtarbet4594 3 жыл бұрын
Oh my god. Am I even smart enough to watch this video?
@josemanuel9305
@josemanuel9305 2 жыл бұрын
All of us have to admit that we can't write xi(ξ)
@MS-cj8uw
@MS-cj8uw 3 жыл бұрын
Thank you ...you mean the evolution of the probability of where we can find the particles but not the shape or profile of its movement in space
@Plams5
@Plams5 2 жыл бұрын
This white background is killing me at 2AM.
@blinkingmanchannel
@blinkingmanchannel 3 ай бұрын
nope...😮
@ProfessorDaveExplains
@ProfessorDaveExplains 3 ай бұрын
Yeah, what?
@blinkingmanchannel
@blinkingmanchannel 2 ай бұрын
Way too hard for me. I thought it would be funny. (That it's way too hard for me.) Your channel is great. It is unusual for someone to actually get into the hard stuff, given the generality of the audiences. All that said, I am super interested in our technological gaps that keep us from building these nano-scale machines. When I first started searching, I thought surely I was nuts because I could not find artificial photosynthesis. (I mean, literally, somebody running ATP synthase -- the little enzyme motor-- in a factory, or at least a lab demonstration project.)
@ProfessorDaveExplains
@ProfessorDaveExplains 2 ай бұрын
Ah gotcha. Yeah it's tricky!
@blinkingmanchannel
@blinkingmanchannel 2 ай бұрын
@@ProfessorDaveExplainsSooooo, since you are willing to correspond directly (I think that's rare and awesome) I have questions, when you have time... (1) Can you help me find the current state of ... Building ATP synthase in a lab or factory? I'm new to this area, painfully, but I thought we'd be farther along in imitating nature for these tiny machines. (I'm noting that we at least have some computer models that calculate the trade-off between reactivity and specificity, but that's in "catalysis" and I'm not interested in "shake and bake" chemistry. (2) I don't see any viable alternatives to the Haber process for cracking nitrogen. There are methods for cracking water, but I consider that "greenwashing." And I'm worried that Haber-Bosch is capital intensive and thus centralized. Not to be a broken record, but why is Nitrogenase so hard to study? If plants need 8 ATP molecules to power Nitrogenase, then we'd better get busy on Question 1, right? (3) I'm looking at the way human beings handle crises, and I'm thinking were gonna need to pull CO2 out of the air at the last minute. What do you think? Have you found any alternatives, even unlikely ones? I'm imagining that the rich countries might conceivably do a Manhattan Project, but even that would require a decisiveness I think we lack. What are you reading these days?
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