Lecture 6: Time Evolution and the Schrödinger Equation
ฝัง
- เผยแพร่เมื่อ 17 มิ.ย. 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 begins with summarizing the postulates of quantum mechanics that have been introduced so far. He then discusses properties of the Schrodinger equation and methods of solving the equation.
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu
His enthusiasm makes me want to learn so much more
thats your problem
good
Neel Modi physics is interesting. Mathe instead...you keep them down that hall XD
Amen. Plus he does have an infectious smile.
Yeah true..
I'm just jealous of these guys' ability to ask interesting questions that seem so logically connected to the subject but i could never come up with.
I'm jealous too but I can ask that kinda question. Maybe the guy has remembered them before.
Although they are smart, they may not be as smart as you think.
Most of these guys studied QM either on their own (e.g. reading books like QM for Dummies or watching TH-cam etc) or took QM course before arriving at MIT. Yes indeed, there are schools that give introduction to QM in High School. So, if they have done that, they are pretty smart.
But realize this may not be the first time they are seeing this. So, smart indeed. But maybe not quite as smart as you might want to believe.
Working the problem sets and the readings help a lot in that regard.
As this is on OCW you have open access to the lectures, recitations, and problem sets as well. If you really want to learn quantum mechanics I highly suggest you look into this wealth of information.
Congratz to the man doing his best to manage the input volume so we can hear the questions ^^
love the way professor Adams explains things, i'm starting to get my master degree in physics and yet by watching these lectures i feel the need to study more,it's like MIT courses makes you realize you need to learn more and more and more... and it's never enough!!!thank you MIT opencourseWare for giving me the opportunity to experience quality courses with these great guys. love you
Did u get it?
xxlblackyoung seconded
@@xxlblackyoung No, of course not. He is just pulling your leg. He is completely clueless. :-)
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@@gaanabajana9343 What's with the spamming?
what i like about his method is that he clarifies all the subtle points so that you don't have anything unclear in your head
These guys always ask very good questions...
Nope, but he encourages them to ask. would you him to say, '' that's a boring question, never ask again!''?
Excellent question as always 😂
He is also very good at understanding what really the listeners would get confused.
No question is a bad question if you are really confused about it. You just need to ask.
@@Saptarshi.Sarkar Yes we totally get that but what he means i guess and i agree with him on that, is the fact that so many questions asked in that class improved my understanding of the concepts, like every question was necessary, without those students this class wouldn't have been the same and the prof was brilliant at understanding the questions as well as elaborating and answering them. It's like everyone in that class played a role in teaching.
The teacher in the clip is very nice - patient, and down to earth.
How to give a Awesome Talk/Presentation ?
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Influence isn't going to solve the problems one faces in the temple labyrinth circuit hell, it is the problem, that who convinces itself that drugs or forces help it or one, but by such, forces and deception it will not cure the sick, disease nor pain nor lift the spirit from its or miseries forces.
Actions may speak louder than words, as decisions succeed declarations, the breadth and prayer heals, that money can't buy one from. The spoiled may struggle to believe it need to fast to meet eternal life, mocking it by feasting and holiday, an angry , resentful its power less, only mammals, but love and truth has not humbled them. Fasting has nothing to argue and war for game. Why woman, man and child, as family need to protest together for the preservation of Life, its clear the fiscal temple labyrinth is hell that the rebellious apostles circuit made for financial power that their soul can't keep up, that greed will take.
Take a shot every time he picks up his bottle and doesn't end up drinking from it haha. Amazing prof.
hahaha
Anyone else transfixed on what he is drinking and how he transports it around the room without ever taking a sip?
Who says it's a drink?
Gregory Whittington thats coffee n either milk or carnation creamer
You have observed a macroscopic quantum mechanic event in action.
i wasn't, but now i am
Thank you very much for making these lectures public. Great topics and explanation !
How to give a Awesome Talk/Presentation ?
Part-1:th-cam.com/video/tOWPfIxZmME/w-d-xo.html
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Influence isn't going to solve the problems one faces in the temple labyrinth circuit hell, it is the problem, that who convinces itself that drugs or forces help it or one, but by such, forces and deception it will not cure the sick, disease nor pain nor lift the spirit from its or miseries forces.
Actions may speak louder than words, as decisions succeed declarations, the breadth and prayer heals, that money can't buy one from. The spoiled may struggle to believe it need to fast to meet eternal life, mocking it by feasting and holiday, an angry , resentful its power less, only mammals, but love and truth has not humbled them. Fasting has nothing to argue and war for game. Why woman, man and child, as family need to protest together for the preservation of Life, its clear the fiscal temple labyrinth is hell that the rebellious apostles circuit made for financial power that their soul can't keep up, that greed will take.
Wish he was my lecturer when I studied this. Makes it so interesting, relevant and clear.
Good job man
Lies again? Samsung Ericsson
How to give a Awesome Talk/Presentation ?
Part-1:th-cam.com/video/tOWPfIxZmME/w-d-xo.html
Part-2: th-cam.com/video/fUAvh_zCats/w-d-xo.html
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Influence isn't going to solve the problems one faces in the temple labyrinth circuit hell, it is the problem, that who convinces itself that drugs or forces help it or one, but by such, forces and deception it will not cure the sick, disease nor pain nor lift the spirit from its or miseries forces.
Actions may speak louder than words, as decisions succeed declarations, the breadth and prayer heals, that money can't buy one from. The spoiled may struggle to believe it need to fast to meet eternal life, mocking it by feasting and holiday, an angry , resentful its power less, only mammals, but love and truth has not humbled them. Fasting has nothing to argue and war for game. Why woman, man and child, as family need to protest together for the preservation of Life, its clear the fiscal temple labyrinth is hell that the rebellious apostles circuit made for financial power that their soul can't keep up, that greed will take.
"mathematicians are sneaky. that's why we keep them down the hall." XD
Valen Cheung that’s what you learned
24:20
These really are great lectures. I'm using them to supplement my coursework and they're really helpful in giving meaning to the equations and solutions i derive in my homework. For instance, I have a midterm tomorrow and i feel pretty good with my ability to handle the math and solve problems; but if asked what my solutions imply i would be hard pressed to answer without the intuition i gain from these vids. This lecture series really helps build my understanding of the material.
Thanks MIT OpenCourseWare!
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explain the point of all this. What is it trying to achieve, why and how?
Try to explain what all these equations are telling about time and how time works.
Without complicated words.
@@pompookgantsu2286 maybe you should just get some more brain cells and learn it yourself.
he is a good prof of quantum
This instructor is worth his weight in platinum!! He is FANTASTIC concerning this somewhat obtuse subject. I am impressed beyond words.
How to give a Awesome Talk/Presentation ?
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explain the point of all this. What is it trying to achieve, why and how?
Try to explain what all these equations are telling about time and how time works.
Without complicated words.
Influence isn't going to solve the problems one faces in the temple labyrinth circuit hell, it is the problem, that who convinces itself that drugs or forces help it or one, but by such, forces and deception it will not cure the sick, disease nor pain nor lift the spirit from its or miseries forces.
Actions may speak louder than words, as decisions succeed declarations, the breadth and prayer heals, that money can't buy one from. The spoiled may struggle to believe it need to fast to meet eternal life, mocking it by feasting and holiday, an angry , resentful its power less, only mammals, but love and truth has not humbled them. Fasting has nothing to argue and war for game. Why woman, man and child, as family need to protest together for the preservation of Life, its clear the fiscal temple labyrinth is hell that the rebellious apostles circuit made for financial power that their soul can't keep up, that greed will take.
Really good explanation - excellent lecturer (Allan Adams); he actually invites questions, repeats them and then gives cogent answers.
It's the first time I've seen someone explain the relationship between eigenstates and Schrodinger's equation. Also how superposition falls out and is effectively a consequence of 'stationary states', therefore unaffected by time. This creates a physical distinction between the quantum world and the classical world, as he explicitly demonstrates; the interface being the 'collapse' of the wave function or 'decoherence' as he calls it, when superposition disappears. Since the wave function is 'all you need' and SE is 'not derived, just posited' makes me think it's a good candidate for the 'God' equation, meaning it fundamentally describes everything that's yet to come into being.
Influence isn't going to solve the problems one faces in the temple labyrinth circuit hell, it is the problem, that who convinces itself that drugs or forces help it or one, but by such, forces and deception it will not cure the sick, disease nor pain nor lift the spirit from its or miseries forces.
Actions may speak louder than words, as decisions succeed declarations, the breadth and prayer heals, that money can't buy one from. The spoiled may struggle to believe it need to fast to meet eternal life, mocking it by feasting and holiday, an angry , resentful its power less, only mammals, but love and truth has not humbled them. Fasting has nothing to argue and war for game. Why woman, man and child, as family need to protest together for the preservation of Life, its clear the fiscal temple labyrinth is hell that the rebellious apostles circuit made for financial power that their soul can't keep up, that greed will take.
OMG...completely impressive!! -- "any function can be expanded as a superposition of eigenfunctions of any operator of your choice", "the special cases -- the Fourier theorem; the general cases -- the superposition postulate."
binging QM lectures, so much better than Netflix
B23
The mind matures faster at the age of 23 , an is continually maturing there after , making it unlawful for Governments or Monarchs or people of the country or religions to take such people under the said age of 23 and form a Military Force or army. Children are not human sacrifices. Good Health to you all. Catching the wind ? Catching the wind on the Twilight B101 . Catch up here with prophet, and profit. In addition to the age requirements for any form of Military Force (offensive/offense) at the more matured age of 23 until further wiser ; please vote for the drinking and smoking age to follow such age; while the disease and viruses ( or hay fever) are due to the practice of the present alcohol use. For There is room for argument , but its only concealing the heart. What is darkened . Therefore the argument is lost. Furthermore, no influenced or drug induced mind could possible have confidence or enough confidence in another to represent its being or well fare, the state of country or land , making thee incapable to vote under chemical influence or contamination . Please vote for drug testing for all voters , and such being the age of 23.Vote B23.We all thank you from the heavenly sky.
When such is understood , and not to be left out, are the facts about those who are in Collage , who the pupil best serves the country , principle an itself , than with a military force and should not be drafted or mandated to serve while in Collage or principle study . For principle protects the heart, heart land and people. Until further wiser.
So please Vote B23
Nice, I can listen to this and not get an headache! Main principles respected, thank god!
Wonderful lecture - manages to work at both the intuitive level and the algebraic level. Thank you!
How to give a Awesome Talk/Presentation ?
Part-1:th-cam.com/video/tOWPfIxZmME/w-d-xo.html
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explain the point of all this. What is it trying to achieve, why and how?
Try to explain what all these equations are telling about time and how time works.
Without complicated words.
I really like this guy!
Me either
As a holder of a computer science degree and another in electronics I bow to the recognition of reality. Circuits and code only do what they are made to do as does your world. So cool. Thanks for the pump.
Influence isn't going to solve the problems one faces in the temple labyrinth circuit hell, it is the problem, that who convinces itself that drugs or forces help it or one, but by such, forces and deception it will not cure the sick, disease nor pain nor lift the spirit from its or miseries forces.
Actions may speak louder than words, as decisions succeed declarations, the breadth and prayer heals, that money can't buy one from. The spoiled may struggle to believe it need to fast to meet eternal life, mocking it by feasting and holiday, an angry , resentful its power less, only mammals, but love and truth has not humbled them. Fasting has nothing to argue and war for game. Why woman, man and child, as family need to protest together for the preservation of Life, its clear the fiscal temple labyrinth is hell that the rebellious apostles circuit made for financial power that their soul can't keep up, that greed will take.
17:43 "A piece of chalk that I am treating as a quantum mechanical point particle." Physics textbooks in a nutshell.
Savings account
Evil works harder, not smarter in fear , scrambling in a pickle concerned in trouble of whether it's going to score or not, an it's not a coincidence that its had the energy and money to fight. Dixie seemed to always be on their side and the interest was mutual between them, Dixie ( or Dollar index exchange) and evil. They never argued about the Interest they paid on the money to fight for the energy and spoil , and they never seemed to stayed together with out it. While migrating the refugees of its breed to its homestead and country , for country cooking ( if you know what I mean) and hospitality for business opportunities ; A share of the American Pie. Market Place.
Unfortunately for those (evil) in a Pickle, the Bank is the Peoples Not the Third Party, an all we need is a Bill of Signatures with a adequate interest rate index on savings accounts, strengthening our Country , Capitalism and Dixie ( or Dollar index exchange ); equality and salvation an American Dream. Hunger makes a great pickle, saves Lives and promotes Health, younger looking skin , less to loan on, or on Vanity and better to help D.i.x.i.e than fear to have the dream, the dream with the Bill of signatures for a savings accounts with interest, so one can retire on and have its leisure...
34:26 did you guys notice that chalk trick
Just for once I want him to say "that's actually not a very good question".
Love MIT OpenCourseWare
MIT is so awesome that I really want to study there!
you are already studying
Kristian Factora haha
Why
superb.. this professor REALLY LIKES his job. Unlike many professor in INDIA
Stellar professor, excellent lecture. I have studied physics myself and got really frustrated. I know everything there is to know about boring physics lectures. This one is motivating, interesting and entertaining. Big up for Professor Adams.
Influence isn't going to solve the problems one faces in the temple labyrinth circuit hell, it is the problem, that who convinces itself that drugs or forces help it or one, but by such, forces and deception it will not cure the sick, disease nor pain nor lift the spirit from its or miseries forces.
Actions may speak louder than words, as decisions succeed declarations, the breadth and prayer heals, that money can't buy one from. The spoiled may struggle to believe it need to fast to meet eternal life, mocking it by feasting and holiday, an angry , resentful its power less, only mammals, but love and truth has not humbled them. Fasting has nothing to argue and war for game. Why woman, man and child, as family need to protest together for the preservation of Life, its clear the fiscal temple labyrinth is hell that the rebellious apostles circuit made for financial power that their soul can't keep up, that greed will take.
Nice Lecture
The explanation and the answer of the question around 57:00 was excellent.
Influence isn't going to solve the problems one faces in the temple labyrinth circuit hell, it is the problem, that who convinces itself that drugs or forces help it or one, but by such, forces and deception it will not cure the sick, disease nor pain nor lift the spirit from its or miseries forces.
Actions may speak louder than words, as decisions succeed declarations, the breadth and prayer heals, that money can't buy one from. The spoiled may struggle to believe it need to fast to meet eternal life, mocking it by feasting and holiday, an angry , resentful its power less, only mammals, but love and truth has not humbled them. Fasting has nothing to argue and war for game. Why woman, man and child, as family need to protest together for the preservation of Life, its clear the fiscal temple labyrinth is hell that the rebellious apostles circuit made for financial power that their soul can't keep up, that greed will take.
For those already initiated in QM I repeat here some comments previously made to similar videos. They may clarify debatable points.
The Schrödinger time dependent equation (STDE) when applied to a wave representing an initial state of, say, an electron bound to a proton and together forming a hydrogen atom, predicts and retrodicts all the future and previous states of the electron wave, in the same fashion than the evolution equations of classical mechanics predicts the movement of the Earth around the Sun. Note that the STDE is energy conservative, that is, the initial state as well as the predicted and retrodicted ones all have the same energy.
As is well known the bound electron has a completely different conduct. Whatever the initial state and in absence of other interactions an excited electron will settle in a stationary state radiating energy (in the form of a photon) along the way. If the stationary state is the ground state the electron will stay there forever (in absence, as said before, of other interactions). Otherwise the stationary electron state is ephemeral and will be abandoned to radiate a photon and assume a new stationary state of even lower energy. This "down the staircase" process repeats until the ground state is reached. There is no manner to adapt the STDE to this physical process. This inconsistency was discovered by none other than Niels Bohr, as can be inferred from the report of Werner Heisenberg. See our note
www.researchgate.net/publication/356193279_Deconstruction_of_Quantum_Wave_Mechanics
After discovering the tremendous inconsistency it would have been natural to announce that the STDE contradicted with physical facts, and ask for a correct equation. I assume as true, but only know from hearsay very long ago, that in Einstein's viewpoint the correct deterministic time dependent wave equation had to be non-linear. References to this historical detail would be appreciated.
It is hard to believe but, against reasonableness and common sense, Bohr decided to adopt the STDE as correct and that continuity, causality and determinism of physical processes were wrong because they contradicted the STDE. Apparently mathematical equations on paper were more relevant than the experience of the whole human race. Then a series of new and fanciful "quantum physical principles" were adopted.
In my opinion the powerful quantum establishment dogmatically defends Quantism and strongly rejects any attempt to correct its misdeeds, even if the correct deterministic time dependent wave equation available.
With best regards to all.
Daniel Crespin
That's utter bullshit. Even a cursory look at the Schroedinger equation tells you that it is not energy conserving.
Savings account
Evil works harder, not smarter in fear , scrambling in a pickle concerned in trouble of whether it's going to score or not, an it's not a coincidence that its had the energy and money to fight. Dixie seemed to always be on their side and the interest was mutual between them, Dixie ( or Dollar index exchange) and evil. They never argued about the Interest they paid on the money to fight for the energy and spoil , and they never seemed to stayed together with out it. While migrating the refugees of its breed to its homestead and country , for country cooking ( if you know what I mean) and hospitality for business opportunities ; A share of the American Pie. Market Place.
Unfortunately for those (evil) in a Pickle, the Bank is the Peoples Not the Third Party, an all we need is a Bill of Signatures with a adequate interest rate index on savings accounts, strengthening our Country , Capitalism and Dixie ( or Dollar index exchange ); equality and salvation an American Dream. Hunger makes a great pickle, saves Lives and promotes Health, younger looking skin , less to loan on, or on Vanity and better to help D.i.x.i.e than fear to have the dream, the dream with the Bill of signatures for a savings accounts with interest, so one can retire on and have its leisure...
You can also get some idea of the "decoherence" problem by determining the TYPE of infinity that the solutions can fall into when this occurs. Is it the smallest COUNTABLE infinity (Aleph Null in Cantor's system) -- the "rational numbers" -- or some higher infinity, such as the number of points on a line, "C" (called this because there is no proof that it is the next-highest type of infinity, though to my knowledge there is nothing between Aleph Null and C), which is, I think, the 'real numbers"? The former has separate, discrete values and the latter does not (its members flow smoothly into one-another with no "edges"). It seems to me that the former has to be true since all observers looking at a given result in a given universe see the same result, while the latter would allow somebody somewhere in that same universe to see a different result (slightly different or perhaps even very different), since the are no rigid "edges" (gaps between) to the values observed.
Huge love and Respect to Professor from Pakistan
Is there a way to get the problem sets? I would very much like to read them
MrArthur0920 The problem sets and solutions are available on the MIT OpenCourseWare site at ocw.mit.edu/8-04S13
I love this the findings will never end . I love that the explanation was always there. Waves and function.we will always be excited over the new great minds . I feel a lot more nobles handed the ones who are finding things first through math . Iqs are not measurements of intelligents. Discovery interest and problem solving through mind over what matters. I love beautiful clarity of all the findings. Life is beautiful with human computations. We are a United commutating astronomical society . Sorry for any of my mathmatical cop outs in life.I wouldn't be able to handle the general delusion in my condition. I'm intrigued by society.Ive been on hold a sleep for 17 yrs and people astound me with there all over intelligents .humar math science neurology. Man I got to learn just so I can play trivial pursuit. I just think people are so much more rich in depth. Your lucky.love your school !!!
It fits, is the point. Great lessons
I like this teacher it lets you catch up
He is a brilliant teacher. Zwiebach is good too, but this guy is better.
The best part of this lecture is how he could never drink his coffee
Thanks mit
11:00 explanation of wave function collapse 12:00 what happens next? 14:30 hook 15:30 good q
18:00 personal note
29:00 non deterministically by probabilities collapse
30:00 !!!!
33:00!!!!
44:00 probability of E !!!!
46:00
51:00
58:00
1:03:00
1:04:00 continuous k
Real food for thought
Whoever did the subs is a godsend
Concerning the discussion of infinite combinations of continuous functions becoming discontinuous at 24:38 I would just add that while it seems merely theoretical it provides further evidence of quanta. We have must have exactly so many wave functions interacting or we can break things like smoothness and continuity which match closely with observation. Limiting behavior defying observation is also what led to the ultraviolet catastrophe, another artifact of quantization.
Nope.
It's just phennomenal way of teaching
Influence isn't going to solve the problems one faces in the temple labyrinth circuit hell, it is the problem, that who convinces itself that drugs or forces help it or one, but by such, forces and deception it will not cure the sick, disease nor pain nor lift the spirit from its or miseries forces.
Actions may speak louder than words, as decisions succeed declarations, the breadth and prayer heals, that money can't buy one from. The spoiled may struggle to believe it need to fast to meet eternal life, mocking it by feasting and holiday, an angry , resentful its power less, only mammals, but love and truth has not humbled them. Fasting has nothing to argue and war for game. Why woman, man and child, as family need to protest together for the preservation of Life, its clear the fiscal temple labyrinth is hell that the rebellious apostles circuit made for financial power that their soul can't keep up, that greed will take.
best teacher everrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr
Thank you for sharing these videos !
I have studied the first one and I enjoyed them a lot !!
I love the way Quantum Mechanics is teached and the very positive atmosphere of these lectures.
I have found one explanation that didn't convice me.
This is at 46 min about, during the solving of Shrödinger Equation (SE). Indeed, SE is simplified by replacing Psi(X,t) by Psi(X,0) and by replacing Energy operator by Energy Eigenstate. This is strange to replace Psi(X,t) by Psi(X,0) under the time derivative symbol because the result would be 0 in that case ... I think that one could apply Shrödinger equation at time 0 instead and therefore replace Energy operator by Energy eigenvalue and find the solution around time 0, then resolve this equation at time Delta t and so on ... and conclude that general solution is the one that is given in this video (perhaps another more straightforward way is possible).
P.S.: sorry for my english, I am french ... nobody is perfect :)
teached naught - taught*
Influence isn't going to solve the problems one faces in the temple labyrinth circuit hell, it is the problem, that who convinces itself that drugs or forces help it or one, but by such, forces and deception it will not cure the sick, disease nor pain nor lift the spirit from its or miseries forces.
Actions may speak louder than words, as decisions succeed declarations, the breadth and prayer heals, that money can't buy one from. The spoiled may struggle to believe it need to fast to meet eternal life, mocking it by feasting and holiday, an angry , resentful its power less, only mammals, but love and truth has not humbled them. Fasting has nothing to argue and war for game. Why woman, man and child, as family need to protest together for the preservation of Life, its clear the fiscal temple labyrinth is hell that the rebellious apostles circuit made for financial power that their soul can't keep up, that greed will take.
A genius can be defined as someone who can redefine the obvious in such a way so as to return something of value that is beyond those who do not understand on this said genius level. This guy nails and proves it. People at work are getting tired of me telling that everything reduces to waves, probability statistics and magic, pure “fing magic”. Not a student but I love this stuff. Don’t stop.
It’s that great full dead juice.
Great lecture
Influence isn't going to solve the problems one faces in the temple labyrinth circuit hell, it is the problem, that who convinces itself that drugs or forces help it or one, but by such, forces and deception it will not cure the sick, disease nor pain nor lift the spirit from its or miseries forces.
Actions may speak louder than words, as decisions succeed declarations, the breadth and prayer heals, that money can't buy one from. The spoiled may struggle to believe it need to fast to meet eternal life, mocking it by feasting and holiday, an angry , resentful its power less, only mammals, but love and truth has not humbled them. Fasting has nothing to argue and war for game. Why woman, man and child, as family need to protest together for the preservation of Life, its clear the fiscal temple labyrinth is hell that the rebellious apostles circuit made for financial power that their soul can't keep up, that greed will take.
I took QM as an elective course in my electric engineering program. I can guarantee that if you had a solid core courses in calculus, diff eq, vectorial calculus and stochastic methods you will succeed and be just fine. I can define QM as a probabilistic method of understanding classical physics and in my opinion is what really happens in our everyday world. Good luck to the ones that are completing the course today. If I can help just let me know. Regards and good luck
'...my life is easier if i don't think about curvy bottoms...' lol (@ 1:15:09)
good catch
Right wingers unite! #wearetheresistance
Spoilt child!
@@user-uu9dm5pz7z Not that you should care particularly, it's irrelevent to QM, but classical liberalism/soft anarcho-capitalism isn't very rightwing. Whilst I think free market capitalism is the fastest way to improve technology and thus quality of life and so in most cases is the best option, I also think that it is the responsibility of a state to provide high quality essential services like healthcare, education, emergency services, and prisons etc. that are free at the point of access, funded by taxes. There are alot of important exceptions where market trends are natrually harmful to everyone. My social liberalism is clearly more 'important' than my slight econmic right-of-centre leanings. Basically don't claim me for your side, if I was American I'd have voted Biden.
@@AlexMcshred6505plus 10 months ago is a long time in politics for me so I wouldn't associate myself back then to now. Besides economic conservatism and social liberalism is left wing in my view which is where you align. I loath social liberalism but I believe in regulating giant corporations to ensure that they do not have too much power which a lot in the GOP and the GOP leaders like to call pure socialism. But if these companies are to dictate/control a nation that is more powerful than the government, I think an entire free market should be limited to free market for an average citizen.
We discussed that we can-with superposition of Eigen state Schrodinger equation solutions make approximately solution to the Schrodinger equation for any state, where the coefficients are the norm squared of the probabilities. Does it make sense in any way to map those coefficients into something like a maclaurin series-so like for each value of the nth derivative (n is an integer) of the function you get a coefficient, with everything else equaling to zero? - to account for the collapsing. But the problem with that would be we won't know which coefficient corresponds to which collapsing. So maybe we could take combination (product) of all such derivatives in all terms-but each degree of derivative evaluated at a different value than every other in a term and than the same variable in every term-in such a way that the symmetry takes away every term other than the one or two that we are able to compute. The combination of all possible degrees of differential functions would mean-okay take everything else as constant and how does this change-remove thay-now everything else as constant and how does this change and so on. While the equation itself would be very long to write down unless someone finds a clever approximate non-polynomial function -but we can still clearly be able to identify the terms that don't cancel out.
Is this the formulation of Max Born interpretation-so that the series continues to exist even after measurement.
Influence isn't going to solve the problems one faces in the temple labyrinth circuit hell, it is the problem, that who convinces itself that drugs or forces help it or one, but by such, forces and deception it will not cure the sick, disease nor pain nor lift the spirit from its or miseries forces.
Actions may speak louder than words, as decisions succeed declarations, the breadth and prayer heals, that money can't buy one from. The spoiled may struggle to believe it need to fast to meet eternal life, mocking it by feasting and holiday, an angry , resentful its power less, only mammals, but love and truth has not humbled them. Fasting has nothing to argue and war for game. Why woman, man and child, as family need to protest together for the preservation of Life, its clear the fiscal temple labyrinth is hell that the rebellious apostles circuit made for financial power that their soul can't keep up, that greed will take.
Allan Adams r really a good prof.
Savings account
Evil works harder, not smarter in fear , scrambling in a pickle concerned in trouble of whether it's going to score or not, an it's not a coincidence that its had the energy and money to fight. Dixie seemed to always be on their side and the interest was mutual between them, Dixie ( or Dollar index exchange) and evil. They never argued about the Interest they paid on the money to fight for the energy and spoil , and they never seemed to stayed together with out it. While migrating the refugees of its breed to its homestead and country , for country cooking ( if you know what I mean) and hospitality for business opportunities ; A share of the American Pie. Market Place.
Unfortunately for those (evil) in a Pickle, the Bank is the Peoples Not the Third Party, an all we need is a Bill of Signatures with a adequate interest rate index on savings accounts, strengthening our Country , Capitalism and Dixie ( or Dollar index exchange ); equality and salvation an American Dream. Hunger makes a great pickle, saves Lives and promotes Health, younger looking skin , less to loan on, or on Vanity and better to help D.i.x.i.e than fear to have the dream, the dream with the Bill of signatures for a savings accounts with interest, so one can retire on and have its leisure...
Operators wear a hat. The prime operators in quantum theory wear a top-hat.
Don R. Mueller, Ph.D. What’s a prime operator ?
Excuse me but the overall phase e^itheta tells you the Phase of. What? This wave function?.. and what does that mean
The partial with respect of time of a wave function \psi(X,0)?
A vivid lecture!
Influence isn't going to solve the problems one faces in the temple labyrinth circuit hell, it is the problem, that who convinces itself that drugs or forces help it or one, but by such, forces and deception it will not cure the sick, disease nor pain nor lift the spirit from its or miseries forces.
Actions may speak louder than words, as decisions succeed declarations, the breadth and prayer heals, that money can't buy one from. The spoiled may struggle to believe it need to fast to meet eternal life, mocking it by feasting and holiday, an angry , resentful its power less, only mammals, but love and truth has not humbled them. Fasting has nothing to argue and war for game. Why woman, man and child, as family need to protest together for the preservation of Life, its clear the fiscal temple labyrinth is hell that the rebellious apostles circuit made for financial power that their soul can't keep up, that greed will take.
The statistical outcomes are based on the perspective, taken at the time of measurement. Perspective is similar to a geometric angle.
Influence isn't going to solve the problems one faces in the temple labyrinth circuit hell, it is the problem, that who convinces itself that drugs or forces help it or one, but by such, forces and deception it will not cure the sick, disease nor pain nor lift the spirit from its or miseries forces.
Actions may speak louder than words, as decisions succeed declarations, the breadth and prayer heals, that money can't buy one from. The spoiled may struggle to believe it need to fast to meet eternal life, mocking it by feasting and holiday, an angry , resentful its power less, only mammals, but love and truth has not humbled them. Fasting has nothing to argue and war for game. Why woman, man and child, as family need to protest together for the preservation of Life, its clear the fiscal temple labyrinth is hell that the rebellious apostles circuit made for financial power that their soul can't keep up, that greed will take.
46-50 : The convertion psi(x, 0) to psi(x,t) is not correct. the partial derivative of psi(x, 0) with respect to time is 0 then!
He missed the assumption that the wavefunction in an energy eigen state will have fixed energy, so, the operator can be applied any time in the future (or past), i.e. at an arbitrary time.
なにこれめっちゃありがたいなMIT最高か
the ideal professor
B23
The mind matures faster at the age of 23 , an is continually maturing there after , making it unlawful for Governments or Monarchs or people of the country or religions to take such people under the said age of 23 and form a Military Force or army. Children are not human sacrifices. Good Health to you all. Catching the wind ? Catching the wind on the Twilight B101 . Catch up here with prophet, and profit. In addition to the age requirements for any form of Military Force (offensive/offense) at the more matured age of 23 until further wiser ; please vote for the drinking and smoking age to follow such age; while the disease and viruses ( or hay fever) are due to the practice of the present alcohol use. For There is room for argument , but its only concealing the heart. What is darkened . Therefore the argument is lost. Furthermore, no influenced or drug induced mind could possible have confidence or enough confidence in another to represent its being or well fare, the state of country or land , making thee incapable to vote under chemical influence or contamination . Please vote for drug testing for all voters , and such being the age of 23.Vote B23.We all thank you from the heavenly sky.
When such is understood , and not to be left out, are the facts about those who are in Collage , who the pupil best serves the country , principle an itself , than with a military force and should not be drafted or mandated to serve while in Collage or principle study . For principle protects the heart, heart land and people. Until further wiser.
So please Vote B23
To be honest, this is such an amazing lecture like we too learn quantum mechanics in class but it seems like those students that are asking questions know more than my teacher.
explain the point of all this. What is it trying to achieve, why and how?
Try to explain what all these equations are telling about time and how time works.
Without complicated words.
Hmm I am not that good in quantum mechanics that I should fully understand the whole lecture, but how much I got it's that here he tells about when a system evolves it means with respect to time, for that we use shrodinger equation while it is rich in concepts like you just can't precisely measure two non-commuting quantities , it gives that probabilities but not an exact number. When he talks about the eigen value , where he tells about superposition of states ,and so many more
@@pompookgantsu2286 Time is that which the clocks show. We tried to explain that to you when you were five or six years old and then again when you were in high school.
@@schmetterling4477 omg this again LMAO you have no clue of what this video is about do you?
I just watched 10 minutes and I didn’t understand a fucking word he said. But yet for some reason I keep watching this shit
So, half way I say time is adjustable through observation. Matches the philosophy that we create what do observe. I’ll be back to edit. Decoherence is an optical term.
FANTASTIC
And so I base my argument to hold my thesis that time is equal to movement times distance and from here forward understand when I look upon a thing in physics thus be applied.
I love how the professor's level of passion for the field grows as the class progresses; clearly amped by the class grasping these counterintuitive and gorgeous mathematical models. It makes me nostalgic for those few short years of intense study, when you could pay to learn what you wanted to learn, in such a focused professional way; several radical departures from the first 12 years.
@MIT What are the texts that are recommended to be read along with the lectures ?
There are four required texts and four recommended texts. See the course Syllabus on MIT OpenCourseWare at: ocw.mit.edu/8-04S13. Best wishes on your studies!
I've some questions regarding this lecture.
1. If the momentum is variable in nature during travelling of any object, then what could be the predictable approximation of Schrodinger wave function ?
2. If the time gets collapsed or the time starts to run backward, I mean reverse, then how the wave function can be expressed ?
3. As severally we read the time gets stopped inside the black hole, then can we really call a particle existing inside the black hole, as in eigen state ?
** If not so can it be possible to apply the time variant wave function at that place for computing energy ?
*** If really we can't apply the time variant wave function, then is it true that the wave nature of any object disappears inside the black hole ?
1. Magic 2. Sorcery 3. Witchcraft
Thank you
Mit open course can make any physics student proud of himself
Influence isn't going to solve the problems one faces in the temple labyrinth circuit hell, it is the problem, that who convinces itself that drugs or forces help it or one, but by such, forces and deception it will not cure the sick, disease nor pain nor lift the spirit from its or miseries forces.
Actions may speak louder than words, as decisions succeed declarations, the breadth and prayer heals, that money can't buy one from. The spoiled may struggle to believe it need to fast to meet eternal life, mocking it by feasting and holiday, an angry , resentful its power less, only mammals, but love and truth has not humbled them. Fasting has nothing to argue and war for game. Why woman, man and child, as family need to protest together for the preservation of Life, its clear the fiscal temple labyrinth is hell that the rebellious apostles circuit made for financial power that their soul can't keep up, that greed will take.
can someone tell me about course book used
Tienen uds un servicio de traducción simultánea?
Newton's equation F=ma is not "just posited." You can derive it using an action principle involving the Lagrangian. Where is the corresponding process for Schrödinger's equation?
Is MIT expensive?
Yep!
Do you get what you pay for?
Absolutely!
The best of the best of the best...
SYSTEMS DYNAMICS; OBSERVERS OBJECTIVE ; WAYS TO ACHIEVE DETERMINIC OUTCOME
Is there a video somewhere introducing the math into quantum physics? I like the abstract stuff, but when it comes to the equations, I'm totally lost.
+Tom Franse The prerequisite math listed in the syllabus is 18.03 Differential Equations (or 18.034 Honors Differential Equations). You can find the MIT OpenCourseWare version of 18.03 at: ocw.mit.edu/courses/mathematics/18-03sc-differential-equations-fall-2011
Thanks!
+Tom Franse It's amazing how much easier this material becomes once you've had linear algebra and differential equations. I watched some over one summer and was just floored at how "hard" the subject was. Took those math courses now it's no problem at all.
questions? when is the first exam? there's one in every class...
For anyone who would like introductory visual representation of the linear algebra, this link is from Yale's BioChem-101 lecture introducing the Schrodinger equation: th-cam.com/video/B4VSqAB_JcU/w-d-xo.html
something like would have to work out constants but using a seperation of variables with 3 functions, 2 of t, 1 of x?
but i started learning PDE last week and havent spent 24 hours since first lecture here...
f ~ exp{(a + bx**2t)}
I’ve never felt dumber in my life.
I have a good question,first there was an experiment done where they watch atoms and in the experiment not sure but they could observes the result of atoms traveling trought light and they where all messy but when observes they where all " calm " witch does work with schrodinger the atoms are messy and calm at the same time BUT my question is get the experiment going watch it and observe , it will be calm after that some how time travel and with the same experiment in theory the result should be the same but if you don't observe it will those atoms will be calm or messy ? is ( easier explanation is would time travel affect the same experiment?)
Savings account
Evil works harder, not smarter in fear , scrambling in a pickle concerned in trouble of whether it's going to score or not, an it's not a coincidence that its had the energy and money to fight. Dixie seemed to always be on their side and the interest was mutual between them, Dixie ( or Dollar index exchange) and evil. They never argued about the Interest they paid on the money to fight for the energy and spoil , and they never seemed to stayed together with out it. While migrating the refugees of its breed to its homestead and country , for country cooking ( if you know what I mean) and hospitality for business opportunities ; A share of the American Pie. Market Place.
Unfortunately for those (evil) in a Pickle, the Bank is the Peoples Not the Third Party, an all we need is a Bill of Signatures with a adequate interest rate index on savings accounts, strengthening our Country , Capitalism and Dixie ( or Dollar index exchange ); equality and salvation an American Dream. Hunger makes a great pickle, saves Lives and promotes Health, younger looking skin , less to loan on, or on Vanity and better to help D.i.x.i.e than fear to have the dream, the dream with the Bill of signatures for a savings accounts with interest, so one can retire on and have its leisure...
22:00 So, why are the superposition principle and linearity different from each other? How can you have a linear wave equation without your wavefunctions obeying the superposition principle? How can the wavefunctions obey the superposition principle without the equation of which they are solutions being linear? Are we making a pedantic distinction between physical properties of a system and the mathematical properties of the equation that describes that system?
tokamak An example of a nonlinear equation that has the superposition principle in it:
sin x = 0
It is nonlinear (as you can readly tell) and its solutions are integer multiples of pi (neatly already homogenous) when considering just the real numbers. If you sum two solutions (equal or different) you get... Another solution. And that is additivity or superposition, at least in a very simple way.
If y and z are two of the solutions of the equation above, one can clearly see that:
sin (y+z) = sin(y) cos(z) + sin(z) cos(y)
Because always when sin(x) = 0 => cos(x) = 1, implying, for instance:
sin²(x) + cos²(x) = 1.
Then:
sin (y+z) = sin(y) cos(z) + sin(z) cos(y)
= sin(y)*1 + sin(z)*1
= sin(y)+sin(z) = 0+0 = 0
As you can see superposition DOESN'T imply linearity. But the converse is true - even if there is no proof here, there is plenty of it elsewhere.
Notice, however that this property doesn't apply to all x in our example (just the solutions, which seems to be good enough) and that it is not homogenous for all x in our example for similar arguments, even if homogenous for all solutions - and that seems, again, to be good enough.
So superposition and linearity are different properties from each other, even if they are somehow related to each other. You can't have a linear equation without the superposition principle, but you can have a nonlinear equation WITH the superposition principle. We are not making a distinction between the properties of a system and the mathematical properties of the equation (but that is not physics or math, it is philosophy: some scientists would say you should make such distinction - Bohr would say that, actually - and other wouldn't); they are different properties.
But your third question, I think, is not answered. What nonlinear wave equations with superpostions as its solutions can exist? I don't think we really KNOW the answer to this question.
I've seen some examples of nonlinear equations with a superposition rule or a superposition principle even. But I don't know of any equation like that in quantum mechanics (I'm not an expert in nonlinear equations, though, and I think one could readly say that as well).
So it would be interesting if somebody could tell me about some examples concernig such topics, just for curiosity - what I readly checked, in a quick search, was not entirely satisfactory or conclusive for me in that matter.
to use a schrodinger equation first the superposition disappears and the wavw function collapses to a single one. so because the wave collapses i believe it needs not support the superposition principle.
Savings account
Evil works harder, not smarter in fear , scrambling in a pickle concerned in trouble of whether it's going to score or not, an it's not a coincidence that its had the energy and money to fight. Dixie seemed to always be on their side and the interest was mutual between them, Dixie ( or Dollar index exchange) and evil. They never argued about the Interest they paid on the money to fight for the energy and spoil , and they never seemed to stayed together with out it. While migrating the refugees of its breed to its homestead and country , for country cooking ( if you know what I mean) and hospitality for business opportunities ; A share of the American Pie. Market Place.
Unfortunately for those (evil) in a Pickle, the Bank is the Peoples Not the Third Party, an all we need is a Bill of Signatures with a adequate interest rate index on savings accounts, strengthening our Country , Capitalism and Dixie ( or Dollar index exchange ); equality and salvation an American Dream. Hunger makes a great pickle, saves Lives and promotes Health, younger looking skin , less to loan on, or on Vanity and better to help D.i.x.i.e than fear to have the dream, the dream with the Bill of signatures for a savings accounts with interest, so one can retire on and have its leisure...
"you stole my thunder"... 15:36
"Any function can be expanded as a super-position of eigenfunctions of any operator of your choice." This is probably the largest take-away from this particular lecture, besides del_t psi = 1/ihbar e-hat psi, which is an interesting statement alone.
what, if anything, is the effect of electron mass of the time evolution? presumably the electron cannot travel faster than the speed of light, so does the mass set conditions on how much space an electron can travel in time given a certain energy value?
malaise69 In quantum mechanics the electron mass is always the rest mass, at high energies you should take into account relativistic effects then change the theory to relativistic quantum mechanics or even more to quantum field theory then the electron now becomes a field and the mass is only a parameter of the theory.
At 48:37, "Does the energy change over time? No." Entropy?
I forget how to multiply fractions from 5th grade, aside from that, where do I start?
Precalc then trig, calc 1,2&3 differential equations for physics, then take nuclear physics courses
very good content sir. thank you .. sir kindly make a video on Bound
States for Potential Wells with no rigid walls.(wkb approximation )
The electrons in an atom are in stationary states. Atom is highly stable structure
Influence isn't going to solve the problems one faces in the temple labyrinth circuit hell, it is the problem, that who convinces itself that drugs or forces help it or one, but by such, forces and deception it will not cure the sick, disease nor pain nor lift the spirit from its or miseries forces.
Actions may speak louder than words, as decisions succeed declarations, the breadth and prayer heals, that money can't buy one from. The spoiled may struggle to believe it need to fast to meet eternal life, mocking it by feasting and holiday, an angry , resentful its power less, only mammals, but love and truth has not humbled them. Fasting has nothing to argue and war for game. Why woman, man and child, as family need to protest together for the preservation of Life, its clear the fiscal temple labyrinth is hell that the rebellious apostles circuit made for financial power that their soul can't keep up, that greed will take.
So...operators only tell you the possible values of the measurement (eigenvalues) will be...
What are the chances of that?
at 45:00 partial derivative of function at t=0 with respect to time,isn't that supposed to be equal to zero?
I know you're long past this question but this answer is for anyone else with the same question. What if the function is e^t? The time derivative of e^t is e^t, right? So the time derivative at t=0 is 1. That is, if Psi(t)=e^t then Psi'(0)=1.
We have to look at what the function is. Usually the time-dependent part of the schodinger equation is given by something like Psi(t)=e^(-iEt/h) so we would NOT get 0 if we took the time-derivative at t=0.
Now, what if Psi(t)=e^(-kt)? Then Psi'(0)=-k.
Etc. etc.. etc..
In other words what he meant is: first take derivative of psi(x,t) and then assign t=0.
Its exactly as Александр Багмутов says.
@@user-cn4qb7nr2mHow about the following step? That equation only applies when t=0, why did he extend this to all time t? 46:00
@@dr.merlot1532 That equation only applies when t=0, why did he extend this to all time t? 46:00
Finally: I will understand this equation.
Savings account
Evil works harder, not smarter in fear , scrambling in a pickle concerned in trouble of whether it's going to score or not, an it's not a coincidence that its had the energy and money to fight. Dixie seemed to always be on their side and the interest was mutual between them, Dixie ( or Dollar index exchange) and evil. They never argued about the Interest they paid on the money to fight for the energy and spoil , and they never seemed to stayed together with out it. While migrating the refugees of its breed to its homestead and country , for country cooking ( if you know what I mean) and hospitality for business opportunities ; A share of the American Pie. Market Place.
Unfortunately for those (evil) in a Pickle, the Bank is the Peoples Not the Third Party, an all we need is a Bill of Signatures with a adequate interest rate index on savings accounts, strengthening our Country , Capitalism and Dixie ( or Dollar index exchange ); equality and salvation an American Dream. Hunger makes a great pickle, saves Lives and promotes Health, younger looking skin , less to loan on, or on Vanity and better to help D.i.x.i.e than fear to have the dream, the dream with the Bill of signatures for a savings accounts with interest, so one can retire on and have its leisure...
1:15:09 I hear you, bro.
SYSTEMS DYNAMICS AS FUNCTION OF TIME DETERMINES ENTROPY ; MUTUAL NETWORK IN ORBIT AND DUE ORIENTATI0N DETERMINES WEATHER PATTERNS
Let's say at an instant we express a wavefunction as a superposition of energy Eigen functions. How can we prove that the time evolution of the wavefunction is given by the sum of the time evolutions of the individual Eigen functions. He said we can do it, but how can we prove it. I mean what if a particular superposition is only valid of an instant. I was solving the Schrodinger equation to prove this, but I am stuck
"Schradinger" - that's driving me nuts.
"Give mathematicians paper and time..."
My life is also simpler when I don't think about curvy bottoms.
@1:15:07
what is shape of box
Great questions from the students.
Only first 8 lecture notes available on the website. Where are other notes?
Sorry, only the first eight lectures notes were given to us by the professor.
@@mitocw Can you please, please, please, please try asking him for the rest?
I really need them.. You've no idea how valuable they are..
Thanks anyway