Your Daily Equation #12: The Schrödinger Equation--the Core of Quantum Mechanics
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- เผยแพร่เมื่อ 13 เม.ย. 2020
- Episode 12 #YourDailyEquation: At the core of Quantum Mechanics -- the most precise theory ever developed -- is Schrödinger's Equation. In this episode of Your Daily Equation, Brian Greene explains where the equation comes from and how it is used.
Even if your math is a bit rusty, join Brian Greene for brief and breezy discussions of pivotal equations and exciting stories of nature and numbers that will allow you to see the universe in a new way.
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I'm only a couple minutes into it where you talk about the equations and I want to say that I love how you add the equations.most people always always always try to dumb it down for everybody and then you never get to find out what the equations are. So thank you very much for adding in the equations that means a lot to us.
I completely agree. Thank you for doing this, Brian
As I sit here contemplating my own field of psychology, I take a break by watching Dr. Greene's daily equation series. Fascinating, absolutely fascinating.
@Dziordan1 Simply to convey the idea that physics, and in particular quantum mechanics and cosmology, are fascinating to many of us regardless of what other professional/academic field we are in. Not sure why your response was so aggressive.
@@Dr10Jeeps - Response was deleted, but I'm guessing it was aggressive because psychology has become, in many ways, less rigorous than it used to be. And it never was particularly good. It has been influenced by politics to an alarming degree, and not many people trust the findings when related to those topics. It often concerns itself with how it's findings affect certain subgroups instead of just stating what is true.
Not only is Professor Greene brilliant, but also a charismatic, funny & great instructor.... his knowledge is so comprehensive, and his facility for teaching & making things seem so simple is akin to Feynman! I miss Feynman so much...
you forgot handsome
Hello Professor,
I was wondering if you could talk about Maxwell's equations with special regard to their physical manifestations.
Also, thank you for this amazing series!
Solid suggestion!
That seems like a pretty complicated equation. The professor really seems to enjoy trying to enlighten us as to how our universe works.
My maths skills are very basic but I'm finding the daily equations very enjoyable and informative thanks to Brian Greene's communication skills.
This was awesome! I did QM in 2nd year physics (in the late 90s), and our lecturers never explained anything about the basis for the Schrodinger equation, nor even really much on its application. They essentially said "trust us", and then tested us on our ability to memorise it and really not much more (I don't even recall them asking us to prove that a given wave function satisfied the equation). So awesome to actually understand the motivation behind it, feel much more confident in understanding how it applies to the development of wave functions - thanks heaps! :D
Phenomenal Professor Brian!! Thanks a lot for your valuable time! It means a lot to all of us who loves physics!! Just unbelievable see those equations coming from you!
very awesome. thank you! I'm no expert at equations, but listening to an expert walk thru them is enlightening and a true delight!
Taking a probability and stats class after having taken modern physics and this makes soooo much more sense to me now. These equations are so beautiful.
i'm not a maths whiz. but to see how your mind able to understands how these ream works just by explaining it using these formulas & equations always amazes me. well done, Professor Greene!!
A teacher for humanity that I enjoyed for years to listen
This is so well explained!! Once again thanks so much prof Greene! :) Huge fan of yours.
An equation a day keeps the dr away?! Really on the bright side, this amazing clear and innovative informative distillation series of a daily equation of Brian's keeps the spirits up..! Thanks from South Africa. Wish I'd had these, and a lecturer like Brian
God bless you, sir
I am a high school student and understood all mathematics of such a great quantum equation thanks to you, sir .
Enjoying your episodes. Thanks!
Best video about the Schrödinger Equation I have ever seen.
An excellent mini-lecture on an interesting subject. Thanks a lot!
Best physics lecture I ever attended. Thanks Brian Greene for explaining it so well
This is so cool and clear! Thanks for these videos!
Thank You for your work. Please keep those videos comming.
Other than the cheesing the wave function onto the potential energy function at the end, this was a great derivation. I can't wait to do this on the whiteboard 8 times before I learn how to do it myself.
I just hope you are aware that the Schroedinger equation is wrong. It doesn't even obey local conservation laws. It is therefor not clear to me how you want to "derive" it from first principles. It's a bad guess by Erwin Schroedinger that was soon replaced by a much better guess by Dirac. The Dirac equation one can "derive" from special relativity with a few additional assumptions. It's still not the complete story, but it gets you much closer to real physics.
I am studying engineering but i have to take a basic quantum physics course and today we were introduced to this amazing equation. Your video explains it so well, i will share the link to this with my professor.
Thank you Dr. Greene. Really nice to see a derivation of the Schrödinger Equation. It makes it feel much more accessible now. And not too bad to follow with your explanation. Not a slog at all, well done Brian!
It seems to me the Schrödinger Equation is like numerical analysis, where it gives a very good approximation. As you say at minute 4 is this video, "it's not an equation *one can derive from first principles." Once we have a First Principles counterpart/equivalent (as in predictive capability) to the Schrödinger Equation, physics understanding will really be moving then.
edit/ Matt, Thailand
I wish , I had him as a teacher in 1977, when my prof did not try to keep awake . He came from US after Ph D but rushed through the derivation .
Hats off , I will call you Greene Guru from now on . Thank you
You gave him a nice name 😊
One of my favourite equations. thanks Brian
Thank you so much sir .It's helping a lot
Dear professor Greene,
I hope you’ll excuse the slightly sycofantic tone in this comment, but I think that you are by far, the greatest intermediary when it comes to turning pretty complicated stuff, into digestable bits of profound knowledge.
I’ve been reading a multitude of popular books on the subjects of physics, quantum mechanics, astronomy etc., but this is the first time I’ve actually come close to truly understanding, what the equations are all about and how they function.
Your videos have done that and I thank you deeply for it.
Thank you, Prof Greene! 🙌
It's been almost 50 years since I had that equation in class, so I don't remember or understand the math. Still, this was very worthy of my time and I thank you for your series.
Awesome series, Professor Greene. I am thoroughly enjoying it. A topic suggestion for a future video: The Euler-Lagrange equation. Many thanks.
Fantastic way to introduce an equation basis on previous fundamental... Your video are greatly structured 👍
Thank you prof.
Thank you for this video! It's much clearer than the derivation I had to memorize in grad school, lol.
So well explained. Thank you very much. Richard
What a brilliant "derivation"! My QM teacher at the time jumped straight to operators, which was a bit confusing for us, given functional calculus was not really part of the standard curriculum and our teacher in classical mechanics was much more occupied telling us stories about his time with Feynman instead of motivating Hamiltonians and such, so had to kind of learn all that by ourselves whilst also taking QM classes.
Excellent walk through, I enjoyed that.
Hi Professor Greene,
My dad and I are really enjoying this series - we discuss it almost every day. My dad remembers his math prof. at the University of Victoria (British Columbia) writing down the Dirac equation - Would you be able to discuss that one on one of your episodes? It would be neat to see the equation that predicted antimatter.
Thank you again for this series!
Such nice story telling. So impressive.
Cant wait!!
Brian, you're a bright dude. Charge your devices before filming. We're at three days in a row with a low battery.
Just a good-natured ribbing.
Keep up the good work. Maths are always fun for me.
These are the best! Thank you!
Love💖from india....
I'm so excited for this...
Thank you!
Best explanation of schrodinger equation
Thanks a lot sir, it helped a lot
Prof Brian...great as always!!!!!!!!!!!!!!1
sir you are one of the great explainer in the world👍
I haven't ever had such an easy explanation!
professor Brian Greene can you please explain about Stephen Hawking's equation on identifying the area of event horizon by the entropy of the black hole.
Yeah! I too want a session on that.
love ya Greene! nice explaination!
thanks for sharing dr b 🍏
Nice episode! These episodes that are more about history, what the equations do or show, and the implications are more enjoyable than those that are mostly math (Schrodinger). Yes - John Bell and Alain Aspect please! (Thanks!)
cool stuff. I like how you do that "projection".
Thanks a lot!
Love love and love.
You're showing the elegance of physics and mathematics altogether.
Now I understand it and don't understand it at the same time. Great episodes! Greetings from Slovenia
I see what you did there.
The demonstration was quite something amazing, even though some parts were little bit vague. According to my own experience Schrodinger's equation is one of the complex equation ever made possible in physics. It's quite interesting and I hope I learn and get it quite decisively in vivid way...I'm still kinda lost some where but I believe I will get there...Thanks
thank you
Fantastic, awesome
You're a great educator Prof. Brian. Could we get a PDF file of your explained equations you've been explaining throughout the daily equations episodes?.
Respect for you :)
Professor, please do a video on the Friedmann equations for the expansion of the universe as well as its derivation.
Well, now I understand why that had us dealing with e to the ix and other stuff in calculus.
I don't know a whole lot of maths but I got really interested from the start.
Good Stuff.
I like your presentations and your books, both of which I persevere with until I get out of my depth, then go back to the basics and start again and hopefully go deeper before I get out of my depth again. I am an aged emeritus prof economist, interested in the application of physics, especially to organisations and their evolution, and think that physics has a lot to offer economics, which I think, is a bit stuck. Like the UK at the moment. Thanks for being interesting.
An option for the next episode might be adding the relativistic parts to the equation, if that of course isn't too out of scope of a single video?
Brian, these videos are awesome. I love learning the equations! I'm at a fairly basic level, so not sure if there is an unsaid reason for it, but please can you try to write your 2's as 2's and your d's as d's, otherwise it can get quite confusing for people like myself who learn very visually rather than mentally. Eg: ih_.d¥/dt = -h_2/2m.d2¥/dx2
Kinda looks like:
ih_.2¥/2t = -h_2/2m.22¥/2x2
Thanks so much an2 please keep these vi2eos coming! ;)
Thanks Brian for this beautiful and clear derivation. Why is it that luminairies like Ulam (if I remember correctly) did not like the equation and said something like that it should not be that good?
Kinetic plus potential energy is also the Hamiltonian.
Gravitation is equivalent or dual to acceleration -- Einstein's happiest thought
Potential energy is dual to kinetic energy, energy is inherently dual.
Energy is dual to mass -- Einstein
Minimizing the action or the difference between kinetic energy and the potential energy -- Lagrangian
When the action = 0 the kinetic energy is equal or dual to potential energy. Gravitation is dual.
Positive curvature is dual to negative curvature, curvature is dual.
The equations of motion (predictions) minimize the action in quantum mechanics, duality.
True.
One can also motivate the Schrödinger equation from the perspective of Hamiltonian mechanics, and replacing "position" with the wavefunction.
This is typical of more advanced "derivations" of Schrödinger's equation.
Didn’t know this channel existed, but I immediately was reminded of Bob Ross. „We can sprinkle in a happy little 2 pi i…“ :D
I'm a 38 year old hairstylist. Lately I've been fascinated with physics, the cosmos, and math.
I'm taking a few courses on Brilliant (brilliant.org) and teaching myself calculus (all for fun! 😎)
While a lot of this is way over my head, in due time I hope I can understand more!
TENSOR would be a great topic. : 😊
I am a post grad student and i have hard time understanding Tensors, it would help me and everyone trying to understand this Masterpiece of mathematics, because of the way you explain this even richard Feynman would love to listen from you 😊
Hello Professor,
i love YDE series!
will you do a big present to all your fans, and make some downloadable PDF of your iPad notes of the lesson? I'm sure we'd all love it!
big thanks and stay safe
How did you include the potential function on the right side of the equation when the left side is still kinetic energy of the particle (product of Planck’s constant and frequency)?
love u boss
Hi Brian,
Is it worthwhile to think it this way..
fabric of space and time are made of many fields and EM is one of those fields.
When a photon or electron is emitted from any device then this particle travels within its field and causes ripples when it moves.
Just trying to understand from your videos if that’s how it works?
Many thanks for running these series
Do something on the General coordinate system used is GR
Hello professor
Am ivan from iraq, i was wondering what is ur perspective or thoughts about the dimension which the universe started at the beginning
Great work Brian, we appreciate you and your level of undrstanding and communication skills. By the way, have you looked into Eric Weinstein's theories?
One can also motivate the Schrödinger equation from the perspective of Hamiltonian mechanics, and replacing "position" with the wavefunction.
This is typical of more advanced derivations of Schrödinger's equation.
It's fascinating that one can take the concepts of advanced Classical Mechanics to construct a comparable formulation of Quantum Mechanics. Energy, linear & angular momentum all carry over.
The same problems which can be solved in closed-form carry over, too: particle in a box, harmonic oscillator, central force, coupled oscillators. So pay attention in your Classical Mechanics Course!
;)
Let's see what is in store for lucky Episode #13!
Central limit theorem! You've gotta say something about Carl Friedrich Gauss sooner or later.
How the heck is it that adding up independent random variables gives the bell curve? How do these independent random variables know that they must add up to form it? And there are certainly many more things to be said about the normal distribution. And probabilities in general.
Sine is equivalent or dual to Cosine, symmetry is dual to anti-symmetry, positive is dual to negative!
Certainty is dual to uncertainty, the Heisenberg certainty/uncertainty principle.
"Imagination (uncertainty, potential ) is more important than knowledge (certainty, actual )" -- Einstein.
Potential energy is dual to kinetic energy, energy is duality, duality is energy. Energy is measured in Joules (Duals, Jewels), waves are dual to particles -- quantum duality. Probability amplitudes are rectified into probability densities -- duality.
Thank you, Dr. Greene! I had some great professors back at University, but your eloquent lecture, here, is excellent.
Yea, let's stay simple for now!
At one point during the early equation discussion, where he got embarassed, I got lost. So I just looked at Brian, to get to know someone whose brain does THIS so easily. Ah! A Beautiful Mind and Soul. (P.S. Although you may reject the last part of that statement! :-)).
Loved it.
it is a PDE (at heart) with a term for uncertainty :) As such the math will work the exact same way as our classical equations although the hbar term resolves to nothingness in terms of formulation when you consider the definition of your potential and the system you are solving... That is funny that is Least Action / Lagrangian mechanics. :)
Excellent video.Thank you. I have problem with understanding one thing.The left side of the equation is based on Photon energy equation (plank's constant x frequency), and the right side is based on kinetic-energy for mass. Can that be explained ?. B.Bolin
Well if you recall the Photoelectric effect you do see that they are related.
This is like "Physics Wheaties"!
Sir...How u record this? If Anybody know inform me
I love Truth. Math approaches fact through theory that we may be incited through a hypothesis, a commendable and worthy study! The wonderous vocabulary will be needing a table of contents visually! You mention "theft" which stands out as something to avoid to strive for the truth of an equation. Many cool expressions of nomenclature lend to a great conversation! Undulations was mentioned, one of my words, and oscillation come to mind. I would be lost if not for some knowledge of The Alfa and Omega. In conclusion, I will need a video of each words meaning to tread above water, okay please? I like math because it is anti-BS, frankly. Richard
I’m in the camp of enjoying all the pretty symbols streaming by as I drool on myself.
Sir will you please tell what is quantum entanglement ?
Almost got to the end before my brain melted
Could you do a video on Schwarzchild's solution to Einstein's equation?
Intrigued by the use of the work ansatz. I know this from German (with capital A) as meaning beginning or start, but apparently in physics it means an estimate of a solution.
@ 8:18 What he is trying to say here (but doesn't show, because there are no axes here) is that he uses position (x) on the x-axis and changes the phase of the exponent by changing time. With a minus-sign and time going forward, the wave moves to the right.
thanks !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! thanks
The entropy equation s log w is simple but interesting.
Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics.
Syntropy is the action of creating a prediction, predictions are used to track targets, teleology.
Teleological physics is dual to non teleological physics (entropy).
Scientists are constantly trying to update or optimize their predictions, this is a general process.