@@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
@@Andy_M.S.c 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.
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.
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.
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
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!!!
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.
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. : )
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.
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 :)
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? 👍
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
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.
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?
I’m 11 years old but some how I understand this! Also, Dave, you are the best UA-cam teacher EVER (I said you are instead of you’re because you deserve more words(and subscribers!))
One note: once u apply separation of variables and u get 2 equation u dont have anymore partial derivativas but "full" derivative with respect to one variable. So the notation is incorrect. Thanks for your videos.
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
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?
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?
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.
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.
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.
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
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.
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
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.
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
Think I'll get back to my trigonometry and polynomial division for now. I'll see you guys in about 50 years
Polynomial division is more painful to me than this.
Lol. If you are thinking about doing physics in university, just remember it only gets harder as time goes on.
@@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
@@Andy_M.S.c 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.
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.
Great job man. Hope you’re doing well.
Still remember my prof teaching this 15 years ago. The colored fonts are incredibly helpful!
Good point. Richard Feynman visualized parts of equations in different colors.
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!
Professor Dave really knows a lot about the science stuff. impressive !
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.
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
Please professor Dave make a whole playlist on QM. Your videos are the only hope for most students) Thank you so much for your work and dedication
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!!!
I recommend ur channel with my friends. They loved it. Ur explanation is superb.
A very profound explanation. Thank you so much Prof. Dave.
I’m in quantum mechanics right now and this is extremely helpful.
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.
thank you😊
I didn't understood 🥲
what... 😀
Dude, I just had a class on this today. Didn't make any sense so thanks for this.
I've gained 40 brain cells by watching this
I've got much a lot!
ive lost brain cells truing to understand lmao
This is so... enlightening! Thank you so much for this series and the whole of your work.
Prof, I started giving thumbs up to your videos before I even see them! Those are invaluable treasures! Grazie!
I have never needed to pause a video so much in my life
YAY Thank you !! I've always wanted the Schrodinger equation fleshed out for me !!!
This is an incredible video. Thank you dearly.
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. : )
Whoa! Way over my head. Ill be back after watching a few other videos so this makes more sense, i promise!
i love this channel so damn much
I am gratefull to find this UA-cam channel
Thanks for making these, I am very excited for the next one!
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.
reconsidering my path in sciences
You should be proud, this is the best QM content on UA-cam.
very happy to see someone is making useful content
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 :)
Woaw, this is really helpful! Thank you prof Dave!
Thanks. This is a nice explanation
this help me a lot in reading and understanding "Quantum Computation and Quantum Information" of Michael nielsen and Isaac chuang
You explain verry well professor Dave. Love your videos.
Extremely nice lecture on QM!
IVE GONE THROUGH 3 PLAYLISTS. AND STILL HAVNT FOUND IT. Still learns some interesting things
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?
👍
Ooooh, Grape, just trying for a bit of lightheartedness, man. Cool your jets!
There was a short clip of water in fhe video. Some flat earthers will say "Water finds its level"
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
@@johnmcclelland649 Not me lol
Flavio Gjoni I know! It was GrapeSkoda.
You are doing god's work my man. Thank you so much.
YOU SAVED MY DAY
When i hear your Vibing intro i forget all my tension it looks like i'm watching cartoon😊
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👍👏❤
You are really very brilliant, sir.
Hope you will be more and more helpful........
yeah.......
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.
Excellent tutorial.
Damn . This what I am looking for!
Please explain the rest!
Thank you very much!
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?
SO CLEAR.
I’m 11 years old but some how I understand this! Also, Dave, you are the best UA-cam teacher EVER (I said you are instead of you’re because you deserve more words(and subscribers!))
Also I have a UA-cam channel called NerdyNinja education
Thank you Dave
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.
Heeeell yeah! Do you have one on Dirac Equation? This is tight!
One note: once u apply separation of variables and u get 2 equation u dont have anymore partial derivativas but "full" derivative with respect to one variable. So the notation is incorrect. Thanks for your videos.
Very clear, thanks!
Awesome & smooth
Just finished physics exam.
Guess I won’t need to know this anymore
Extremely helpful
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
Sees thumbnail: Aight imma head out
Hi teacher I used your Chanel everyday. Cause I just wanna be like you 🤩🤩🤩🤩🤩 I’m from Chile 🇨🇱
omg I cannot thank you enough😭 thank you soooo much!
This is a great brain exercise
Why the hell did I click this video thinking I might have the tiniest clue of what Dave is talking about?
I want moooore. I need more
Hi professor can you do schrödinger equation for a 3d particle please....thank you
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?
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?
12:27 I don't know why this is so satisfying
Why is it valid to separate psy into phi and ksi? You wouldn't be able to do that for most functions.
To separate the (x,t) function into configuration space variable only, and time variable only.
Can you debunk the Michelson-morley test? I've been seeing this one creationist trying to peddle this on his channel
Oh my god! I swear the book just threw the equation at me and said it wasn’t derivable! I finally get it!
Clean and crispy
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.
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.
but why. did you not derive the. time dependent schrod eqn. ?
thank u for saving me boss
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.
Time is done by the time machine in London's museam
Awesome.
Waiting if he gets to 1 Million
at about 10:13 mark, why when doing the integration with out any limits is there no constant added on to the end.
I think he skipped steps to make it less complicated. I believe the constant of integration works out to be zero
HEY CAN U MAKE PRACTICE PROBLEMS IN MATHS PLZZZZ.
I wish I understood what Prof Dave is saying???
U explained shit that my professor couldn't done in the last 4 lectures
7:00 Why does the operator V lose the phi and xi? Does it not have partial derivatives in it?
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
Did this get reuploaded?
yeah, i made a really stupid error and someone caught it so i decided it was early enough to just print again
@@ProfessorDaveExplains Was it just the delta symbols?
yeah, so dumb of me!
@@ProfessorDaveExplains but amazing......🍏
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.
Why don't you just make a playlist on differential equations and all this quantum mechanics chapters.
quantum mechanics goes in the modern physics playlist. i will eventually do differential equations and that will go in the mathematics playlist.
@@ProfessorDaveExplains ohh thanks professor Dave. what about this video? which playlist does it goes in?
modern physics
I think I understood some of the words.
Love the new haircut
What's important is,Will it make a good t shirt quote?
Hi
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
👏
I want episodes about electronics
i'll do electrical engineering and computer science at some point, probably next year
First.
Therefore, sexiest.
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.
Good at the sex, tho?
@@tsvetanstoychev655 Oh, God, no.
Awful.
The earth is flat AND round at the same time
You're a little lost, kiddo.
@@ProfessorDaveExplains earth = cat
@@ProfessorDaveExplains im just messing around lmao
What happened to his cat ?
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
Is this the world’s hardest equation?
One of them yes
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
best
yuh yeah yuh yeah yuh yeah