Your Daily Equation #12: The Schrödinger Equation--the Core of Quantum Mechanics
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- Опубліковано 8 лют 2025
- 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
I am a college student. While rushing through my physics course I couldn’t succeed in getting the intuition of (kx-wt). It made me hopeless to understand the concepts to their bones. Now I feel like I have it. I can’t thank you enough🙏🌷
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
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!
My maths skills are very basic but I'm finding the daily equations very enjoyable and informative thanks to Brian Greene's communication skills.
A teacher for humanity that I enjoyed for years to listen
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!!
That seems like a pretty complicated equation. The professor really seems to enjoy trying to enlighten us as to how our universe works.
Best physics lecture I ever attended. Thanks Brian Greene for explaining it so well
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.
Best video about the Schrödinger Equation I have ever seen.
I’m currently in a 3000 level modern physics course for electrical and aerospace engineers and the topic is currently Shrodingers wave function. This is a really good overview of the physics. Man I would love to take a physics course with Dr. Greene. Not bashing my own Prof but it’s been quite a bit more challenging trying to conceptualize and compute problems from this topic compared to relativity which was taught earlier in the course. I found SR to be pretty simple and much more intuitive which I suspect most people do. Many of these daily equation videos are very helpful as they are very well explained and delivered in a way that helps gives intuitive life to the symbols and operations.
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!
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 😊
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.
very awesome. thank you! I'm no expert at equations, but listening to an expert walk thru them is enlightening and a true delight!
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!
Awesome series, Professor Greene. I am thoroughly enjoying it. A topic suggestion for a future video: The Euler-Lagrange equation. Many thanks.
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.
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.
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.
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.
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
An excellent mini-lecture on an interesting subject. Thanks a lot!
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
This is so well explained!! Once again thanks so much prof Greene! :) Huge fan of yours.
You're showing the elegance of physics and mathematics altogether.
Fantastic way to introduce an equation basis on previous fundamental... Your video are greatly structured 👍
God bless you, sir
I am a high school student and understood all mathematics of such a great quantum equation thanks to you, sir .
This is so cool and clear! Thanks for these videos!
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.
Best explanation of schrodinger equation
Enjoying your episodes. Thanks!
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! ;)
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?.
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 for your work. Please keep those videos comming.
Now I understand it and don't understand it at the same time. Great episodes! Greetings from Slovenia
I see what you did there.
Other than the partial derivative dels looking like the numeral 2, this was clear and easy to follow.
Thank you for this video! It's much clearer than the derivation I had to memorize in grad school, lol.
Excellent walk through, I enjoyed that.
I don't know a whole lot of maths but I got really interested from the start.
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.
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!)
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
One of my favourite equations. thanks Brian
Great lecture! Thank you!
Thank you, Prof Greene! 🙌
Love💖from india....
I'm so excited for this...
it's also THE equation of structural chemistry
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.
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?
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
Thank you so much sir .It's helping a lot
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?
Thank you prof.
Such nice story telling. So impressive.
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!
Professor, please do a video on the Friedmann equations for the expansion of the universe as well as its derivation.
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 😊
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?
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.
I haven't ever had such an easy explanation!
sir you are one of the great explainer in the world👍
These are the best! Thank you!
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.
Prof Brian...great as always!!!!!!!!!!!!!!1
love ya Greene! nice explaination!
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
Respect for you :)
So well explained. Thank you very much. Richard
Love love and love.
@ 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.
That's very interesting how energy is related to frequency, and momentum is related to SPATIAL frequency (I'm coming here from an optics/imaging background, not a quantum mechanics background).
The funny thing about Maxwell's equations though, is that you either have the time-dependent equations where there are two time derivatives, OR you have the time-independent equations, obtained assuming the exp(jwt) time dependence, which contain the -k^2 term in place of the two time-derivatives. But you NEVER have one explicit time derivative AND one jw "time derivative" TOGETHER, like on the LHS of the Schrodinger equation at 27:00. This always confounded me about the Schrodinger equation compared to Maxwell's equations. In this respect, it seems like Schrodinger's equation is half in the time domain and half in the frequency domain.
BTW, one thing I always wondered about Schrodinger's equation is, I wonder if it predicts the Fermion-ness (or, the potential for interactions) of electrons compared to Maxwell's equations, in which many waves can only superpose, but never actually interact or collide. Maybe it's related to Schrodinger's equation being an eigenvalue equation, as opposed to Maxwell's equations, which are just plain vanilla wave equations. Or maybe an approaching electron is represented by a potential function: V(x,t) = 1 / (x - vt) and perhaps the electron has to scatter in order to prevent the potential function from becoming singular.
Another thing I've always wondered about Schrodinger's equation is how the Laplacian is like "kinetic energy" for a wave. The Laplacian measures the bulginess of a field, so for a Gaussian "bell shaped" function, the Laplacian I think would be greatest at the peak of the Gaussian, so that would be a point of high kinetic energy? I've always wondered about that, how bulginess of a function relates to kinetic energy of the corresponding particle. And it also seems to me that the greater the Laplacian, the more localized the function is in configuration space, which I think means the broader it is in momentum space? There's just so much to unpack for Schrodinger's equation compared to Maxwell's equations. I think you could do 20 videos exploring all the different facets of the equation.
The Schroedinger equation is neither relativistic nor is it even physical. It doesn't tell you anything much about the real structure of the actual theory. Maxwell's equations are mean field approximations of the equations of quantum electrodynamics, so that's where you would have to start... with a book on QED, if you wanted to understand what is really going on here.
Thanks a lot!
Thank you, Dr. Greene! I had some great professors back at University, but your eloquent lecture, here, is excellent.
Hello. I follow your courses and I admire you, I am not a specialist in the field of physics... The love for physics came later ..I am working on a project let's call it "Sequential Projection". How would you achieve the formation of an electromagnetic band, based on perception sensors?I work a lot, I encountered notions that are not so familiar to me... I dare to go this way if we can work on this wonderful project. I hope it will be a good start. Thank you!
I’m in the camp of enjoying all the pretty symbols streaming by as I drool on myself.
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!
Does the probability outcome of the schrodinger equation predict the energy of a particle at a particular location and time?
Cant wait!!
Mr. Brian, has the quantum Schrödinger equation been tested on the additional dimensions in superstring theory, and how difficult is this work? Who among the scientists conducted such research, and where did the research reach results? I hope you pay attention to my question, Mr. Brian, and I thank you
thanks for sharing dr b 🍏
Fantastic, awesome
Good Stuff.
cool stuff. I like how you do that "projection".
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)?
Thanks a lot sir, it helped a lot
The wave function is not a function, it is a section in a complex line bundle over the physical space. To truly understand it requires deep understanding in topology.
So you have acquired a deep understanding of a false equation? That's so cool. Your Mom must be so proud of you. ;-)
Is it a bit strange that the law of conservation of energy is "assumed" in the Schrödinger Equation while the law can be momentarily violated in quantum physics?
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.
I"m not smart enough to be here but i'm glad you guys let me listen anyways
Thank you!
15:02 ,what’s the frequency of the covid 19 viruses outer shell and the frequency of the viruses phage
Is i time? I think i = time. That sure explains why time is missing from all of quantum physics: it's actually right there in i.
Predictions, increasing syntropy is dual to increasing entropy.
Teleological physics is dual to non teleological physics.
Equations, mathematics, models are used to make optimized predictions, target tracking, teleology.
All equations, equivalences, similarities are dual A = B, thesis is dual to anti-thesis -- the time independent Hegelian dialectic. Syntropy is the integration, convergence or union of information to form predictions, expectations, priors.
Integration (syntropy) is dual to differentiation (entropy).
Symmetry (Bosons) is dual to anti-symmetry (Fermions).
Respected sir, the only question that eat up my brain from many years. Why the wave equation need to be complex no, what does it signifies mathematically and physicaly. Can't we have real no wave equation??
Well, now I understand why that had us dealing with e to the ix and other stuff in calculus.