Modelling just ONE electron "orbiting" its atom animated using the 2D Schrödinger equation
ฝัง
- เผยแพร่เมื่อ 14 มี.ค. 2021
- The beautiful Schrödinger equation calculates the waves that describe where an electron exists around an atom. It can only give the probability of locating the electron shown by the white shaded areas and this "opens the door" to the difficulty of interpreting quantum physics!
A different form of Schrödinger's equation can give the quantum energy levels of the electron.
The animation time steps through the simplest numerical calculation of the 2D Schrödinger equation.
The electron (described by a "wave packet" and seen as the white circular blob) is "released" initially having a vertical upwards momentum (given by the frequency of real & imaginary parts of the wave packet). Further info. including a page with code to plot a 2D wave function is here: sites.google.com/site/logiced...
The electron has a single negative unit of charge and is shown being attracted towards a single positive charge in the centre of the screen.
The wave function of the orbiting electron is shown evolving in time as a result of its electromagnetic attraction towards the nucleus, its own momentum and Heisenberg's uncertainty principle. The Schrödinger equation is sufficient to model all these phenomena.
The model plots ripples in the wave function that are a little like those filmed of a real electron by Mauritsson et al. shown in this TH-cam: • Scientists in Sweden f...
Ref. journals.aps.org/prl/abstract...
Seriously, animations like this are the key to keeping mathematics almost tangable.
With all the comments about interpreting this animation of a 2D Schrödinger model atom I had some comms from an old physicist who sent the following observations of the model/animation:
It is interesting to see the initial wave packet evolving into a combination of stationary states associated with possible (discrete) energy levels.
There is evidence in the animation of outgoing spherical waves.
A bit difficult to see but they are there I think. This is to be expected as we have a kind of collision of the electron wave packet with the fixed central charge.
So, in the end, when the process has settled, we have a superposition of a number of stationary states at discrete energy levels, plus an outward traveling spherical wave (or cylindrical wave as the model is 2-D) going off the infinity. It is not high energy scattering.
The initial wave packet is moving rather slowly (low energy) and is drawn into the centre settling there in a superposition of 'stationary' states represented by the circles around the centre.
There still should be some scattering I think, and this is just visible, but it not like scattering at high energy in a direct collision, when the outgoing waves would dominate.
Hope that adds to the interest of how to interpret and understand quantum physics!
If you get an external cavity laser and fiddle with the mirtors it makes paterns very similar to this.
This is a really well created animation. Thank you :)
Thank you :)
A masterpiece of scientific art! Intuitively presenting the unintuitive! I will save this video and watch it whenever I contemplate the electron. Please ignore the negative comments. The tiny ants shake their little fists at the elephant, connecting comprehension to the incomprehensible. Thank you!
That's electron probabilistic cloud around the nucleus. Not orbiting around atom like clasical?
Yes; it’s superposition is spread out in an area defined by its quantum wave mechanics.
yes :)
Pretty cool animation, kudos!
Thanks
Strongly elegant to me, from my ignorance.
I would like to know a little more about the music, which reminded me strikingly of Moondog, something certainly unexpected, and probably completely unrelated. Very pleased with the enjoyable experience and the representation of a really difficult concept!
this truly is the first video where there is just ONE electron "orbiting" its atom animated in 2D using the Schrödinger equation!
beautiful!
Beautiful!
Thank you
Where are all the cats, alive or dead?
That depends… 😉
Both alive, and dead. Which one you see depends on which of the Many Worlds has become your reality.
I like that! Chemistry feels like some sort of simplification to me.
its a wave,
no its a particle.
it's electron man
It's both
amazing
With lots of previous comments about the original video title which was "This is just ONE electron ..." and all the issues that statement raised, especially in the context of quantum physics, particles and wave functions, etc. I've changed/improved the title to "Modelling just ONE electron ...". Thanks for discussions. 👍
cool would have been to see the evolution propagated into the future faster and faster to get some idea of what its 'end state' looks like.
yes - later screens required and work to do ...
Hmm…I’d like to see how it would look like in more complex atoms, like beryllium for example. It also has P orbitals along with s, not to mention angular and radial nodes
Hydrogen has a full set of p etc. orbitals as well. They are just not the ground state.
This video doesn't show the ground state either btw.
The title with "orbiting" is all about seeing the development of the initial wave packet which was not related to any particular set of energy states. Eigen vector and value analysis of the frames would be useful/interesting.
Well do it yourself and post it on UT .
@@logicedges Oh, I must have misunderstood the video then. Sorry about that
@@landsgevaer I must have mistyped. I actually meant electrons, not orbitals
Seems like the youtube algorithm began to like this, cool video though.
Keep up making cool stuff. Do you study in college or have studied?
Where's the theremin music and William Hartnell's disembodied head?
So this is showing the probability distribution over time right? As electrons are waves and the point like particle only becomes apparent when it interacts with another quantum field.
It took 3 years for someone to come along and not know what quotation marks mean.
It should emit one or more photons at some point, right? You started it in a fairly high energy state.
I think not necessarily - this time dependent Schrödinger equation model only provides the evolution of any given wave function / wave packet over time without changing energy. The initial wave packet can be built from a spectrum of energy levels which I've not calculated - some work to do there!
One would need to include em field in hamiltonian to get the photon emission, im not sure but I think it would be much more complicated calculation.
What initial state did you put the electron in? Clearly not an eigenstate, but also seems to be a wave packet which is asymmetrical with respect to the proton. I'm assuming here that the nucleus, which isn't explicitly shown, is in the center of the simulation.
Yes - the attractive -1/r potential is centred in the middle of the screen.
Further details used for the initial state of the wave function / wave packet are in the code in the "How to draw ..." page sites.google.com/site/logicedges/how-to-draw#h.caqf7q1byr0y
A sinusoidal wave constrained/modulated with a 2D Gaussian function placed so that its initial motion is perpendicular to the radius - I was imagining placing an electron near a proton and then "throwing" it into an "orbit" and seeing how the system would develop.
@@logicedges yes that makes more sense. That's a beautiful and practical illustration of how a wave can nevertheless produce what we classically consider to be orbital motion. Well done!
👍
If still interested I've added a comment with an observation (8th June)
1 down. 117 to go.
Ok, so it's LIKELY to be there but is it actually ORBITING the nucleus? and what reference point do you use for it to be orbiring since you can't use a reference point on the nucleus.
One can compute its orbital momentum (as a super position at least). That still kind of justifies the word.
The model places a "nucleus" centred in the middle of the screen.
Can you post the code for your simulation? Your work is pretty amazing!
Yes That would be very cool to try in python etc - amazing work !
This page provides an overview and link to code: sites.google.com/site/logicedges/the-schrödinger-equation
@@logicedges : Got it. Thanks. In Python, a plus.
👍
The "How to draw" code for a 2D Schrödinger equation model is now here:
sites.google.com/site/logicedges/how-to-draw#h.caqf7q1byr0y
Hope you like.
so this is what we are made of, flushy twlirs
Yep. The video below shows how this translates into our perception of solid objects:
th-cam.com/video/yqLlgIaz1L0/w-d-xo.html
Hello
The 'orb' form at the beginning, was that a infinitely-uncertain momentum 'situation'?
Simply put, what were the initial parameters for the equation which gave such a pure sphere?
The initial condition / wavefunction is a plane wave of a fixed frequency and phase for a momentum moving vertically upwards on the screen and the magnitude/amplitude is the visible circular / 2D Gaussian function.
The Gaussian function is spread out so that there is some uncertainty in the position and some uncertainty in momentum. This would satisfy the Heisenberg uncertainty principle which the Schrödinger equation also maintains. One of the things that makes quantum physics beautiful.
@@logicedges Why did you choose an electron moving vertically upwards?
And if it's a plane wave, why is the wave function shown circular?
@@bjornfeuerbacher5514 It isn't a plane wave since he applied a gaussian envelope. The phase information is not shown in the video.
Not sure how he handled the third dimension, if he speaks of a 2D gaussian.
@@landsgevaer He wrote himself that it is a plane wave above. So why don't you tell him that he is wrong about that instead of me?
The whole animation is 2D (that's stated already in the title of the video), there is no third dimension involved.
@@bjornfeuerbacher5514 That sentence continued a bit further, I think. He wrote it is a plane wave *with a gaussian amplitude*.
I don't think a plane wave can have a gaussian amplitude, so that is a modification.
Are those white areas where the electron probably is/time?
yes, see recent comment
If you did solve for the energy, would this electron be in the (constant over time) ground state?
I think it's likely to be a combination (superposition) of various states since the shape that develops is quite messy. This numerical model is dimensionless with no physically scaled values (i.e. c, m or h) and simply showing the dynamic movement of the wavefunction from an initial position/state. Calculating and displaying the components and energy levels that could make up the messy blob(s) would be another good/fun project to do!
@@logicedges Right, if I recall correctly if it were in an energy eigenstate then it'd be a standing wave. At least I think I learned that for the 1D infinite square well and think it generalizes. I hope you keep making these for different contexts. Really interesting to see and think about.
👍
Yes the quantised energy levels correspond to wavefunctions that have nodes and a finite integral
- the only valid solutions have |ψ|² decaying to 0 as x and y tend to infinity. Quantisation being a natural property of the equation. Brief further info. is at sites.google.com/site/logicedges/the-schr%C3%B6dinger-equation
@@cademosley4886 If still interested I've added a comment with an observation (8th June)
I need mr schrodinger's equation to calculate the size of my brain since it darn sure isn't big enough to grasp what I'm looking at here but at least it's big enough to know it's seeing something pretty darn cool...
🤣
Is this why people call it an electron "cloud"?
yes
There are models of visible photons with electrons orbiting an anti-electron (positron) and both of them smeared out over an area somewhat. I call it the disassociated electron theory, and it perfectly explains pair production and many other mysteries.
Pair production is not a "mystery", where did you get that idea from?
And electrons don't simply orbit positrons - both have the same mass, so they could only orbit each other simultaneously. And those orbits would not be stable anyway.
So your alleged "perfect" explanation has already two glaring errors.
You need to do more research.
One model (that he is obviously refering to) views the photon as orbiting electron/positron pairs.
Attitudes....jeez.
@@dananorth895 I have a PhD in particle physics, but nevertheless I never heard of that model. Where did you get that from?
@@dananorth895That is precisely the theory I referred to. And Pair Production is in fact a mystery because no physicist understands how it works. They just know if one aims a powerful Triton laser at a proton rich metal like lead, uranium, gold etc., they produce one electron and one proton. Obviously we are witnessing the photoelectric effect, which can only mean that there was an electron absorbed from the photon, with a different electron emitted on the far side. There are models showing that a position (anti-electron with no nucleus) somehow has the equivalent of two protons associated with it. In this case, one is absorbed by the metal while the other is emitted on the other side. We aren’t magically creating matter from energy, we are witnessing spallation and the photoelectric effect. That Japanese student who modeled shells in various particles like protons in the 80s might be able to explain it better. In the meantime I suggest watching the computer rendition of the photon traveling through the tube as captured by the “world’s fastest camera” a few years back. We definitely see magnetic lobes in the photon, with plumes of plasma erupting off the surface and being recaptured and looking very much like this video only much faster. And since I’m on that subject, take note of the shocking fact that the tube lights up BEFORE the photon passes through, meaning the photon is like a lantern that produces the light and is not the light itself!!!! The only suggestion I have is that it is like a small sun where the photosphere is producing light via some kind of incandescence, and the light in this case is very excited infrared photons. If I’m wrong, then we are witnessing a plasma made of quarks or fermions or some smaller order of matter. Either way, E = MC2 simply means that energy is just highly excited matter which is smeared out in what I call a dissociated state and thus barely registers as a force with our current detectors. And by extension, matter is slow or even frozen energy.
If still interested I've added a comment with an observation (8th June)
Don’t you mean orbiting a nucleus?
! 😮 ... yes ! ...
Video title has been tweaked
So we are seeing the different points in3D where the electron could possibly be? Brighter ares more likely? Whats the significance of the start and end of the video?
Yes the white areas are the probability the electron is at that location. It is orbiting around a positively charged point which represents the atomic nucleus. The start and end are schroedinger's equation, which describes this probability, and is the equation used to run this model.
yes, density of white colour indicate probability of locating ( & confirmed by @Kvltklassik )
And with this time dependent Schrödinger equation model the start and end points are in fact completely arbitrary. The initial state shown is simply a particular shape of the wave function "chosen" to have "an electron" moving from a constrained circular region with a small momentum moving upwards in the screen. This momentum is governed by the frequency and phase of the real and imaginary parts of the wave function.
More detail of the initial state of the animation will be provided soon.
@@logicedges could you also make a video that instead shows 100 electrons following their own path? Or would it just appear random and uninteresting? I love this video anyway, thanks.
Multi-particle models are harder to do - and slower to compute!
Happy you like the video :)
Details of the initial state / wave packet set up in "How to draw ... (example codes)" page here sites.google.com/site/logicedges/how-to-draw#h.caqf7q1byr0y
That reminded me of a Tidal Disruption Event! (A.K.A. When a star gets pulled into a black hole.) Very cool, thank you.
So what's the quantum number of that electron after capture? Looks like a hybrid state.
Good question :)
Indeed hybrid - which in some ways makes interpreting it all more complex I think including the meaning of "orbiting" which has raised comments. Details of the initial state to be provided ...
Details of the initial state / wave packet set up in "How to draw ... (example codes)" page here sites.google.com/site/logicedges/how-to-draw#h.caqf7q1byr0y
Wouldn't the final state be a phased locked standing wave related to electron energy and fixing its orbit?
P.S. the transition waveforms might also be interpreted as absorbtion/emission perturbations/interactions which potentially can cause jump in energy/orbital levels.
If still interested I've added a comment with an observation (8th June)
What does it look like animated in 1D?
good question - in many ways "similar". Here is a very good set of 1D examples of a wave packet in different conditions:
th-cam.com/video/v0UIGl4cTD0/w-d-xo.htmlfeature=shared
@@logicedges Huh. I was half joking. Half serious-curious. I can't decide if that's 1D, 2D or 1.5D.
Now simulate 5+ electrons around a nucleus
Not possible. When two electrons are in the same orbital the system is no longer solvable *exactly.* Means there is no equation derivable to plot.
However, you can still calculate the wavefunctions numerically using the Perturbation Theory, which considers each electron around the nucleus individually, then accounts for the repulsion between the electrons and you get an approximate solution. My guess is he'd have to do this each frame of the video as a function of time.
if he keeps using 2d space then the shapes the electrons will take on will not look the same as they would be in 3d space
If still interested I've added a comment with an observation (8th June)
I even doubt the shape of an atom
the shape of an atoms is ... strange to say the least ! 👍
I curious because it seems like energy is lost in the wavefunction from the lateral wavepacket dispersion... how is this possible with quantized orbitals? Am I not understanding the simulation, but it seems apparent that their is energy lost in this simulation and if that were true eventually the electron orbit would decay and fall intot he nucleus, which is not what happens.
Yes, it can look like energy is being lost as the wave packet spreads and "slows down". However the area under the wave function remains constant while its shape is changing and "swirling" in a complex manner and the total energy of the system is being conserved. From 40 seconds into the animation the swirling cloud is rotating stably clockwise. with an energy "value" that is equal to the value at the start of the initial wave packet shape. Wave functions give us the best "view" of an electron which are always spread out - so it is very difficult to "see" what the speed or momentum of the electron is.
The momentum is given by the wavelength of the real and imaginary parts of the wave function, which can be seen to be stable in the animation, although the latter part of the animation is only showing the modulus squared (a^2 + b^2) of the wave function (a + ib). 🤔👍
@@logicedges : The total energy would also be uncertain because of the finite time intervals between frames of the simulation.
If still interested I've added a comment with an observation (8th June)
Nice, thanks. I'll check it out. I haven't gotten to grad quantum yet so I figure it will make more sense as I do. I think I get the gist of what you're saying though.
@@kgblankinship I didn't think about the del(E) >= h_bar/2(del(t)) part, but yeah that makes sense.
A lot of this is still kind of unintuitive for me, only just got out of undergrad quantum.
The music though
yes the music is original
This really was very nice.
I have a few questions.
What algorithm did you use?
Did you treat the Schrodinger equation as a diffusion equation?
Anyway, very nice.
Thank you. I did a basic numerical time-stepping method of the Schrödinger equation.
The logicedges "How to draw ... (example codes)" has the basic code: here:
sites.google.com/site/logicedges/how-to-draw#h.caqf7q1byr0y
and an overview here:
sites.google.com/site/logicedges/the-schr%C3%B6dinger-equation
If still interested I've added a comment with an observation (8th June)
Next video: How to catch an electron
Can you tell me what the music is ?
Recorded soprano sax. and keyboard. Let's call it "Orbiting Electron" 👍
Bomfunk Mc's - We are atomic electronic supersonic
@@logicedges wait, it's original?
Now do 2
I'd like to get the code used for the animation.
A general code that can be easily put into js/c/java/py/... is here sites.google.com/site/logicedges/how-to-draw#h.caqf7q1byr0y
Everettian
There's the eye again.
Wait, this is just geometry... with extra steps
In terms of modelling a wave (though with an imaginary component) - yes - But there's never a "just is" aspect to quantum physics!
Seems like everything is
"geometry"? how?
Is my universe a miniverse?
@@cHAOs9 interesting question depending on how you interpret that
Now show us in 3D.
It's just on my 2D screen but i cannot not see it in 3D
The model is only the 2D version of the Schrödinger equation rather than the 3D.
i.e. only calculating ψ(x,y) in V(x,y) rather than ψ(x,y,z) in V(x,y,z).
Is there any other way to calculate a form in 2D with it's Depth? 😝@@logicedges
Ehm, judging from the code, this is not just animated in 2D but also only modeled in 2D cartesian coordinates? So the third (z) dimension is omitted?
That essentially turns the geometry from spherical into circular/cylindrical?
If so, this has nothing to do with an atom of course: the nucleus would be a line/tube instead of a point/sphere. Nothing to do with physics even: for example, in order for the (classical) electric field to be divergencefree in 2D, the potential needs to be like ln(r) instead of 1/r.
It would make more sense to model in 3D and then project/slice in order to depict it in 2D; or to use spherical/cylindrical coordinates such that you can impose rotation symmetry around one axis but still model it as a 3D system.
Unless I am mistaken what was done here, of course.
Yes - your clarification on the details of the animation are all correct :)
The title - which has proved to be complex - or an over-simplification - which I guess is inevitable (take your pick!) doesn't give all details.
So:
"Electron" refers to the plausible wave packet that could represent an electron that is not in a particular state;
"orbital" refers to the evolving spread of that wave packet
that has only been calculated by
the 2D Schrödinger equation Cartesian coordinates and remains constrained (or attracted) to
the midpoint of the plot area using
a 1/r potential ... such as an atom ... but only in a 2D cartesian coordinate space.
I hope that provides near final(?!) clarification of the words in the video title of, yes, a difficult to grasp "object"! 😮👍
@@logicedges I think that it might be best to remove the word "atom" and replace it with a 2D 1/r radial potential well... 😉
@@landsgevaer 👍 Certainly and sadly the simple words in the title add to the complexity of understanding the animation. It's looking as tho' this will be solved by making the title more opaque and harder to understand. 🤔 ... 🥴
If still interested I've added a comment with an observation (8th June)
This is just the opening credits to Doctor Who slowed down!
So this could be a representation of a hydrogen atom, with its single electron and a lone proton nucleus.
Yes - but with spread of wavefunction developing and eventually settling to a more stable state ... it's a transition from a somewhat arbitrary initial condition.
How does hydrogen atom generate so many Spectral lines?
Simply from all the possible transitions between each pair of energy levels of the electron orbitals given by the Schrödinger model of hydrogen or the standing waves Bohr atomic model.
Very cool looking, but a lot different than a real atom
👍 Yes - only a 2D wavefunction evolving and at the strange timescale of attoseconds. I guess it's difficult/impossible(?) to "see" an orbiting electron.
@davidhabd9721 could you please elaborate on "different from real"? What would real look like then?
@@logicedges Mengapa hanya terlihat gelombang elektron, bukankah harusnya dia bersama higg boson..
@@cammancaid799 the model is simply of an electron being affected by a radial electric field - as in a simple hydrogen atom. (No Higgs bosons used in the model)
@@logicedges I went I SAW I came back.
Toroid
After 3 years, am I really the one who's commenting that electrons do not orbit atoms? They orbit the nucleus and together they form an atom.
Not quite - see previous comments/etc. which have clarified the video title to be edited to ... "orbiting" ... "its atom". It's easy to slip up on title texts when publishing on youtube without an editor ... and then there's comments ... :/ ;)
While yes, you’re of course correct, I think this is a little pedantic and it’s safe to say most people know what they meant.
@@deathvideogame Correcting _fundamental_ mistakes is pedantic?
"When the wise man points at the moon, the monkey looks at the finger.."
@@oosmanbeekawooThank you for this excellent description of the “pedantic monkey.” Lol
🙏🙏🙏🙏🙏
Biblically accurate electron
Whatever that means.
no, scientifically accurate election
uhh... what??
Have in mind what the case would be if we were in "Classical Mechanics" (Electrodynamics). We would see how the point charge spins towards the origin of the potential, but here, in Quantum Mechanics we are seeing how the probability density function of locating the electron evolves in time
A proton is a collection of 1836 expanding electrons and add a bouncing expanding electron makes a hydrogen atom. “G” calculated from first principles- the hydrogen atom- in 2002. “The Final Theory: Rethinking Our Scientific Legacy “, Mark McCutcheon for proper physics.
holy crap david randell bot is here too @@davidrandell2224
It's only your imagination, reality is different.
Electron is squishy? Yeah no I'm staying away from quantum physics
It's not as hard as you might think.
@@kgblankinship if it isn't hard, then it's squishy :P
@@ShimrraJamaaneThe more energy you feed into it, the less squishy it gets. But its momentum gets out of hand.
it’s not that it’s hard, it’s just getting plain weird lol
Tell to this electron to be there or not to be there! Enough with its absencepresence.
An electron is like a liquid that spreads out all over the place. Two electrons don't mix though so its kinda like one electron is oil and the other is water.
@@DERIVATIVES-mh6ej Can we speak finally about the gender of the electrons? This should increase our social credit, instead of searching closed contours of probabilistic integrals of some unknown but humble wave function.
@@christopherneufelt8971 wtf are you even talking about, Chris?
Very unconvicing.
How so?
@@af6462 How am I not convinced? Beats me.
@@gibbogle wow riveting stuff, then why comment?
@@af6462
Because it's a mock-up based on an equation not an actual video of the true situation. It might be useful but it does not convinced me any theory concerning what subatomic particles are, if they actually are particles, or if any of the theories are remotely close to the true reality. But please tell me. What did you learn by watching this video? What part of any theory does it prove or even support? I don't believe atoms are made of particles. I believe the basic components are formless. No form whatsoever. Because atoms give structure... atoms give form. Then how can subatomic particles have form? So what would you call this visual representation? The formless nature of courage? The formless nature of love? Fear? hope? Cowardice? We recognize those things when we see them but they are not made of atoms they have no form. Play arise from things which are living creatures which are made of atoms therefore having form. And it seems evident that atoms give form. But why should we assume that the basic components of the atom have the same characteristics? The so-called subatomic "particles". How could such particles have form if they have no atomic weight? In what way has it been proven that they have any mass at all.
@@af6462 Why do you?
Do you actually understand this or are you reading a script? Electrons don't "orbit" as though they were planets. That mischaracterization was put to rest decades ago. What year are you living in?
You don't get it. The Schroedinger wave equation gives an equation for the time evolution of the statistics of electron location over time. What is shown in the video is the transient response of an electron initially located over a particular region, that is having an initial probability distribution. The electron orbitals are merely the steady-state solution. The simulation approaches the orbital steady state over time. What is remarkable is the presence of ripples in electron location that matches attosecond measurements given in the paper described in the link.
It's quite tricky getting a few words in a title just right - so orbiting was used mainly because the Schrödinger equation was developed to show the "orbit". The title having "orbiting" in quote marks would be better.
Op understands very well and is using it as a metaphor. Don’t be so literal and so fast to put someone down, you like the idiot in this case.
Video title has been tweaked
man, sit down and take a breath, c'mon, the title was just referring to the "orbit" of a electron as their multiples possibles states visualised by the formula, and not the "orbit of planets". you better than this dog, get serious for a sec
A proton is a collection of 1836 expanding electrons and add a bouncing expanding electron makes a hydrogen atom. “G” calculated from first principles- the hydrogen atom- in 2002. “The Final Theory: Rethinking Our Scientific Legacy “, Mark McCutcheon for proper physics.
Okay crackpot
david randell bot is EVERYWHERE ITS INSANE LMAO
@@ebog4841 Reading exceeds your brain power: go back under your rock.
@@ebog4841 What have you read of said book: nada. 2 months later and you are still “bogged “ down reading your comic books.
@@davidrandell2224 nice pun!