Best video on spherical harmonics yet. This video actually gives you an intuition for why those seemingly alien-looking blobs look the way they do. Mathematically, the spherical harmonics are the angular solution of Laplace's equation in spherical coordinates and form an orthogonal basis for all functions on a sphere (sort of like a generalization of a Fourier series.)
@@captainhd9741 Laplace's equation essentially takes on the spatial part of a wave equation, so its solutions are just like what you'd get if you solved the wave equation, but these solutions will be static (the partial with respect to time would yield zero, recovering the general form of Laplace's equation), so this is how I think of Laplace's equation giving you the set of standing waves given a set of boundary conditions. By setting up Laplace's equation in spherical coordinates and solving it via separation of variables, you find that the angular part gives you the spherical harmonics and the radial part given by the Bessel functions, which together form the set of all possible standing waves on a sphere (hence the name spherical harmonics.) By solving Laplace's equation in polar coordinates (2d analog of spherical coordinates) you find that the angular part is really just a set of sines and cosines, which form the basis of a Fourier series. Extending this notion into three dimensions, the spherical harmonics end up forming a basis of a 3-dimensional Fourier series, and just like a regular Fourier series, you can decompose any function on a sphere into a linear combination of spherical harmonics. The intuition behind this I don't fully understand, I just learned this without really getting an intuition for why it works. If you want to dive into the math, I can leave a few papers discussing this in detail: mathworld.wolfram.com/SphericalHarmonic.html cs.dartmouth.edu/wjarosz/publications/dissertation/appendixB.pdf
@@northernskies86 Thanks a lot for taking the time typing this up! All I am on equal footing with is that the Laplacian operator in spherical coordinates for the Schrodinger equation has solutions that are spherical harmonics. I still didn't really understand the stuff about Fourier series and I am also unfamiliar with Laplace's equation as this is a first exposure for me.
they look they way they do because they are eigen-shapes of rotations around the z-axis with eigenvalue exp(im theta). which is very much like Fourier basis functions exp(ik x), which are eigen values of translations x -> x + dx with eigenvalue exp(ik [delta x]). The reason spherical harmonics are more complicated is because, while (x, y, z) translations commute, general rotations do not. I like the nodal-line break down, because it captures a major property trivially: the number of nodal lines is not changed by an arbitrary rotation, so each set of 2L + 1 shapes is closed under rotations, e.g., if you rotate the z-axis to the x-axis, the new shape is a linear combination of m = +/- 1. From that you should convince yourself that summing the |squares|of all the "m" shape for fixed L results in a perfect spherical shell. Also, you can see that L=1 can be mixed to represent x, y, z...that is: they are the true shape of vectors, while m=0 is a scalar (doesn't change under rotations), and from there...the 5 L=2 shapes represent that shape of rank-2 cartesian tensors that are symmetric, and traceless in all indices. This can be taken to higher N, so N=4 will give you insight into the generalized Hooke's Law, relating the rank 2 stress and strain tensors with a rank-4 "spring constant = elasticity tensor". No, really, master Y_lm and anisotropic mechanical/dielectric materials, atomic orbital, nuclear shapes, computer game graphics, and so on will just make so much more sense.
@@AnimeRaves Mathematically, the spherical harmonics are the set of solutions to the angular part of Laplace's equation in spherical coordinates. The angular part of the Hydrogen atom wavefunctions is the spherical harmonics because the Coulomb potential is only dependent on r, so it won't affect the angular component of psi. The angular part of Schrodinger's equation for Hydrogen is the angular part of Laplace's equation, and that as we know has the spherical harmonics as the solution set. Spherical harmonics actually show up everywhere in physics, from vibrations on a sphere to radiation patterns, and as you mentioned atomic orbitals. Somewhat intuitively speaking, the energy levels of Hydrogen must be standing waves around the nucleus, and spherical harmonics are basically just harmonics on a sphere, so that's why they show up.
Classical physics suggests that sine waves are created by oscillating locations of force emitters. So mass emits gravity, a charge emits electrostatic charge. As "particles" of mass or charge oscillate (move in a circle in space), a fixed point will experience a variable force over time, as the charge or mass moves closer towards it and then further away from it. Mapped from the perspective of the fixed point, the force of the oscillating mass or charge becomes a sine wave. Therefore, if we have a sine wave, we may extrapolate backwards, and suggest the source is an oscillating "thing". Just so, if we measure peculiar arrangements of harmonics in charge, which we do, we can extrapolate backwards and infer that these harmonics are generated by oscillating particles exhibiting charge. In other words, spherical harmonics are a real thing, in the world of atomic charge, and from such patterns we extrapolate the idea of many oscillating particles of charge, moving in a certain way. It's very odd, because as I have said, the idea that waves are caused by oscillating "things" is very much classical physics, not quantum mechanics. Therefore spherical harmonics are actually a wave function based on classical physics, and not deduced by the mathematics of quantum mechanics. Quantum mechanics has come to accommodate spherical harmonics (the actual existence of them, which cannot be denied) by describing the oscillating movement of particles, but this is, on a philosophical level, a refutation of the core idea of quantum mechanics, which is that wave harmonics are actually just the probabilities of discreet particles colliding with each other. Spherical harmonics in charge suggest that waves are not just mathematical representations of probabilities.
Hahahaha I had previously watched a MUCH LONGER VIDEO about this but ended up with VERY LITTLE IDEA of what these things really looked like. This short video has made things SO MUCH CLEARER!
@@quantumvisionsumunster8208 that's a tall order. What are the key ideas? For some ppl, it's nodes and waves on a sphere, for others is irreducible representations of SO(3), for others it's an eigenvalue-of-rotations problem! idk, maybe those are all equivalent, but they sure sound different.
@@DrDeuteron I just plot the equations for complete Fourier system on the sphere S2. Its the usual (boring) stuff, but I tried to make explicit the idea of nodes. Euqations are standard, see e.g. en.wikipedia.org/wiki/Spherical_harmonics. For more general representations, see www.quantenspiegelungen.de/en/subdimension-line-u3/topology-of-the-quantum-dimension/topology-and-quantum-nodes/
This is an extremely useful video! Conceptually, I am trying to visualize how each spherical harmonic can be a superimposition of traveling waves to form the standing wave oscillation on the sphere. For example, I can visualize how in the m=0, l=1 harmonic, this could be visualized in two dimensions as two single wavelength traveling waves originating at the north pole, traveling on opposite sides of a circle and crossing each other at the south pole to return to the the origin, and the average wave intensity would be similar to the oscillation you show with the node at the equator. What seems harder to visualize is how real traveling waves could form the m=1, l=2 scenario where the nodal lines are perpendicular on the sphere. I read for example that this might be like circularly polarized traveling waves on the sphere with the 90 degree rotated components of the waves accounting for the two 90 degree separated nodal lines, although I am struggling to determine if that is the correct way to visualize it or if it is actually due to some other pattern of traveling waves. Any chance you could comment on the correct way to visualize the m=1, l=2 as traveling waves?
In the video, I show the real part of Y_lm exp(i w t), which either has a cos(+|m| \phi + w t) (right moving) or cos( - |m| \phi + w t) (left moving) term, which leads in the time dependence to the "rotating bubble" without further deformation, since time only appears in this term. Thanks for the question!
I started thinking about this after watching a singer shatter a wine glass by singing at it using its resonant frequency. Putting more energy into it than it could handle. A bit like a photon escaping. Then I considered how the glass could flex, and how physical limitations would cause any oscillation that wasn't at a resonant frequency to be self canceling, since the ends of the oscillation wouldn't meet. Then I imagined the limitations in 3 dimensions and how with something as small as an atom, unaffected by the macro universe, there would be basically no damping, so this "wine glass" could ring virtually forever.
This is awesome. The semi-circle transformation kinda confused me. I thought it was sliding at first, but looking at one quadrant shows it to be streching and shrinking
good catch. This is why mass distributions don't have a "dipole moment"--it's just a translation of the center-of-mass. also, since z is arbitrary, can you figure out which combinations of of m = +/- 1 are shifts in the x and y directions? (Hint: ask chemist).
While spherical harmonics are the eigenfunctions of the hydrogen atom to describe its state, which are the eigenfunctions for the other 117 chemical elements (helium, etc.)?
Thanks for the clear and concise conceptual explanation! Additionally, when somebody can't fit into their favourite pair of jeans anymore, we could say "you're looking a bit too 2nd spherical harmonic for those". :D
it depends on the phase (prolate or oblate). Note that the L=2 harmonics of a shape *are* it's moment-of-inertia tensor, so it captures both your weight and, wait for it, "how your body carries the weight").
@@DrDeuteron Haha cool! Yeah I learnt just enough about it to implement for diffuse global illumination from an environment map, but one day I'll circle back and try to understand it fully. :)
@@leighkite1164 another comment points out the similarity to Fourier series, where you project an arbitrary function onto pure sine and cosine functions,-standard in so many field. It really is the same thing, just on a sphere instead of a string or a plane. Have fun with it. See "Wigner d-Matrix" for a deep dive.
For those That prefer a mechanical analog you can look at harmonics of a guitar string and such. The video I present is another mechanical method of quantizing a system. It is one of two methods where structures can actually be produced. th-cam.com/video/wrBsqiE0vG4/w-d-xo.htmlsi=waT8lY2iX-wJdjO3 Area under a curve is often equivalent to energy. Buckling of an otherwise flat field shows a very rapid growth of this area. If my model applies, it may show how the universe’s energy naturally developed from the inherent behavior of fields. Under the right conditions, the quantization of a field is easily produced. The ground state energy is induced via Euler’s contain column analysis. Containing the column must come in to play before over buckling, or the effect will not work. The sheet of elastic material “system” response in a quantized manor when force is applied in the perpendicular direction. Bonding at the points of highest probabilities and maximum duration( ie peeks and troughs) of the fields “sheet” produced a stable structure when the undulations are bonded to a flat sheet that is placed above and below the core material.
There is no need for a mechanical analog. Spherical harmonics are just harmonics of 3d pressure waves in any fluid. You can create those shapes with sound. A loudspeaker is a dipole in the air medium, and this creates waves who's shape is the first harmonic, because the presence of one low and high pressure point is what polarity is. The 2 pressure zones have a spherical influence, and this creates the motion of a pulsating sphere where high and low pressure areas alternate, creating the shape of the first harmonic. The reason this also happens with atoms is because the universe too is a mechanical fluid. Fluid dynamics alone creates all there is. Electrical charge is just mechanical pressure inside the fluid that is space, and fluid motion of any kind produces toroidal force fields, regardless of it being water, air or space, I which case they are simply labeled as magnetic fields.
Is there a connections between civil engineered trusses and atomic structures? This video shows a natural quantized effect using a version Euler’s Contain Column Theory? This video of an engineering test models the quantum physics problem called “Particle in a Box”. The wave function is used to predict the location of quantum particles, atomic structure and molecules. th-cam.com/video/wrBsqiE0vG4/w-d-xo.htmlsi=J5jCMxq3pRe_P-gG Very stable trusses and truss core panels have been fabricated using the process shown in the video. The video shows how materials naturally respond to induced stresses in a “quantized“ manor. The process’s load/deflection’s sawtooth curve with its exponential fit in the engineering study shows the previously unknown bifurcation between quantum jumps. The effect has been used to make light weight structures and shock mitigating/recoiled reduction systems and earthquakes isolation systems. The model shows why with the, exponential load increase and loss of resistance at phase change, quantum jumps are so very fast.
Do you have research for dynamical behaviour of the earth? Do see oval shapes in objects in space so ...they perhaps can be round/sphere on another time frame. (perhaps in thousand years). Do see a lot of static anal;yses of the earth and also mostly local. Do not see many global analyses of the earth and its shape for instance ....volume changes in relation to volcansim. Earthquakes and how they move along the earth and insde the earth.
We have 2l+1 modes with l nodal lines in TWO dimensions (surface of a sphere). Overtones are related to vibrations of a string in ONE dimension. The groud tone is given by l=1, the first overtone l=2, etc. See www.quantumreflections.net/subdimension-line-u2/standing-waves/spectrum-of-a-guitar-string/
More general: www.quantenspiegelungen.de/en/subdimension-line-u3/topology-of-the-quantum-dimension/ see also my technical comments on www.quantenspiegelungen.de/wp-content/uploads/QuantumVisions.pdf (starts at p. 89)
i studied mindlin plate theory at uni last year, i wonder if these shapes are dictated by the boundary conditions. i just know this is going to be a rabbit hole for me 😂
Just look into you textbook. Indeed, spherical harmonics give a complete basis on the sphere. Not much choice left. Generalization to spin is shown here: www.quantenspiegelungen.de/en/subdimension-line-u3/topology-of-the-quantum-dimension/topology-and-quantum-nodes/
that's what orbitals are. And btw, the language and interpretation of modern physics is false. Atoms are just those spherical harmonics in a premarital fluid that is the fabric of space , there are no electrons, protons or anything like that. They are are just mathematical artifacts and forcefully upheld as concepts, but completely obsolete and not real. They are just the number of low pressure and high pressure areas of the magnetic fields who's vibration produces the orbital shapes The spherical harmonics are 3d dimensional em waves which are produced by a bunch of equal magnetic fields sticking together. If you take a magnet and draw a line perpendicular to its field lines, you get the shape of the first harmonic. if you take another one of equal size and strength and let it stick together, you get the second harmonic and so on. Sound waves make the exact same shape, a dipole make the first harmonic. Finally, the whole universe is just a fluid in motion. You can simulate the entire universe just with fluid mechanics by postulating a fluid that is modelled as being composed of a single particle with Planck's length as it's radius, and 0 properties except radius and density. The fluid has an internal pressure and seeks pressure equilibrium. It also has no friction or 0 viscosity. Electrical charge is just a local pressure that is lower or higher than the equilibrium or the medium. Fluids form toroidal force fields when their balance is disturbed. If you push any volume of fluid, the density of it's destination is increased because you push more fluid into a volume where there already is just the amount of fluid to be in equilibrium, so that area then becomes higher pressure or density. The old location of the displaced volume of fluid leaves a void behind, which is low pressure. The fluid is filling the void left behind, so from all around the void except from the direction you push it in, fluid rushes towards the center of the void. The opposite happens to the high pressure zone, fluid flows away in all directions except from where it came from. In a 3d fluid simulation, the fluid motion traces out a toroidal force field. That is what a magnetic field is. The point is that the universe itself is just a fluid, and fluid mechanics alone creates everything there is. The 100s of hypothetical particles of mainstream physics are just specific force signature of specific subatomic interactions which of course is why they are quantized. But they are not matter, just forces. Matter is exclusively made up of magnetic fields, and the number of electrons and protons just corresponds to the number of fields that make up the atoms. Electricity is not electrons flowing, it's fluid flow who's energy is a multiple of the one that is mapped to the electron, but what's flowing is not actually matter, it's just fluid who's kinetic energy was previously part of the movement that produces the harmonics.
Best video on spherical harmonics yet. This video actually gives you an intuition for why those seemingly alien-looking blobs look the way they do. Mathematically, the spherical harmonics are the angular solution of Laplace's equation in spherical coordinates and form an orthogonal basis for all functions on a sphere (sort of like a generalization of a Fourier series.)
Could you explain this point more?
@@captainhd9741 Laplace's equation essentially takes on the spatial part of a wave equation, so its solutions are just like what you'd get if you solved the wave equation, but these solutions will be static (the partial with respect to time would yield zero, recovering the general form of Laplace's equation), so this is how I think of Laplace's equation giving you the set of standing waves given a set of boundary conditions. By setting up Laplace's equation in spherical coordinates and solving it via separation of variables, you find that the angular part gives you the spherical harmonics and the radial part given by the Bessel functions, which together form the set of all possible standing waves on a sphere (hence the name spherical harmonics.) By solving Laplace's equation in polar coordinates (2d analog of spherical coordinates) you find that the angular part is really just a set of sines and cosines, which form the basis of a Fourier series. Extending this notion into three dimensions, the spherical harmonics end up forming a basis of a 3-dimensional Fourier series, and just like a regular Fourier series, you can decompose any function on a sphere into a linear combination of spherical harmonics. The intuition behind this I don't fully understand, I just learned this without really getting an intuition for why it works. If you want to dive into the math, I can leave a few papers discussing this in detail:
mathworld.wolfram.com/SphericalHarmonic.html
cs.dartmouth.edu/wjarosz/publications/dissertation/appendixB.pdf
@@northernskies86 Thanks a lot for taking the time typing this up! All I am on equal footing with is that the Laplacian operator in spherical coordinates for the Schrodinger equation has solutions that are spherical harmonics. I still didn't really understand the stuff about Fourier series and I am also unfamiliar with Laplace's equation as this is a first exposure for me.
they look they way they do because they are eigen-shapes of rotations around the z-axis with eigenvalue exp(im theta).
which is very much like Fourier basis functions exp(ik x), which are eigen values of translations x -> x + dx with eigenvalue exp(ik [delta x]).
The reason spherical harmonics are more complicated is because, while (x, y, z) translations commute, general rotations do not.
I like the nodal-line break down, because it captures a major property trivially: the number of nodal lines is not changed by an arbitrary rotation, so each set of 2L + 1 shapes is closed under rotations, e.g., if you rotate the z-axis to the x-axis, the new shape is a linear combination of m = +/- 1.
From that you should convince yourself that summing the |squares|of all the "m" shape for fixed L results in a perfect spherical shell.
Also, you can see that L=1 can be mixed to represent x, y, z...that is: they are the true shape of vectors, while m=0 is a scalar (doesn't change under rotations), and from there...the 5 L=2 shapes represent that shape of rank-2 cartesian tensors that are symmetric, and traceless in all indices. This can be taken to higher N, so N=4 will give you insight into the generalized Hooke's Law, relating the rank 2 stress and strain tensors with a rank-4 "spring constant = elasticity tensor".
No, really, master Y_lm and anisotropic mechanical/dielectric materials, atomic orbital, nuclear shapes, computer game graphics, and so on will just make so much more sense.
I do not believe that a better visualization exists on this topic, and we are graced to have access to this free of charge. Thank you!
this is one of the most profound videos i've ever seen in years of watching quantum videos
This is truly amazing. The only jump you made which I couldn’t follow was from the vibrating wave to the circle diagram.
Yeah
It was kinda going from two dimension to three..
Still wanna know
How this works in quantum.
@@AnimeRaves Mathematically, the spherical harmonics are the set of solutions to the angular part of Laplace's equation in spherical coordinates. The angular part of the Hydrogen atom wavefunctions is the spherical harmonics because the Coulomb potential is only dependent on r, so it won't affect the angular component of psi. The angular part of Schrodinger's equation for Hydrogen is the angular part of Laplace's equation, and that as we know has the spherical harmonics as the solution set. Spherical harmonics actually show up everywhere in physics, from vibrations on a sphere to radiation patterns, and as you mentioned atomic orbitals. Somewhat intuitively speaking, the energy levels of Hydrogen must be standing waves around the nucleus, and spherical harmonics are basically just harmonics on a sphere, so that's why they show up.
@@northernskies86 Bzzzz, nerd alert!
Classical physics suggests that sine waves are created by oscillating locations of force emitters. So mass emits gravity, a charge emits electrostatic charge. As "particles" of mass or charge oscillate (move in a circle in space), a fixed point will experience a variable force over time, as the charge or mass moves closer towards it and then further away from it.
Mapped from the perspective of the fixed point, the force of the oscillating mass or charge becomes a sine wave. Therefore, if we have a sine wave, we may extrapolate backwards, and suggest the source is an oscillating "thing".
Just so, if we measure peculiar arrangements of harmonics in charge, which we do, we can extrapolate backwards and infer that these harmonics are generated by oscillating particles exhibiting charge.
In other words, spherical harmonics are a real thing, in the world of atomic charge, and from such patterns we extrapolate the idea of many oscillating particles of charge, moving in a certain way.
It's very odd, because as I have said, the idea that waves are caused by oscillating "things" is very much classical physics, not quantum mechanics. Therefore spherical harmonics are actually a wave function based on classical physics, and not deduced by the mathematics of quantum mechanics.
Quantum mechanics has come to accommodate spherical harmonics (the actual existence of them, which cannot be denied) by describing the oscillating movement of particles, but this is, on a philosophical level, a refutation of the core idea of quantum mechanics, which is that wave harmonics are actually just the probabilities of discreet particles colliding with each other.
Spherical harmonics in charge suggest that waves are not just mathematical representations of probabilities.
finally, these shapes as the harmonics of a sphere make sense. thank you!
Hahahaha I had previously watched a MUCH LONGER VIDEO about this but ended up with VERY LITTLE IDEA of what these things really looked like.
This short video has made things SO MUCH CLEARER!
Welcome to QuantumVisions. Ma aim is to show key ideas only.
@@quantumvisionsumunster8208 that's a tall order. What are the key ideas? For some ppl, it's nodes and waves on a sphere, for others is irreducible representations of SO(3), for others it's an eigenvalue-of-rotations problem! idk, maybe those are all equivalent, but they sure sound different.
@@DrDeuteron I just plot the equations for complete Fourier system on the sphere S2. Its the usual (boring) stuff, but I tried to make explicit the idea of nodes. Euqations are standard, see e.g. en.wikipedia.org/wiki/Spherical_harmonics. For more general representations, see www.quantenspiegelungen.de/en/subdimension-line-u3/topology-of-the-quantum-dimension/topology-and-quantum-nodes/
This is the clearest explanation I've seen to date.
Thanks and welcome to QuantumVisions!
Amazing contribution to understand the geometry behind spherical harmonics!!!
Best visual explanations I've ever seen!!!
Thank you I've never understand spherical armonics and this videio it's so intuitive and easy to understand.
This is a pure pleasure to watch! You deserve more subs!
Just subscribed immediately after watching few seconds of video! What a clear and crisp explanation!
I wonder such an awesome video has so less views. Thanks for this.
Good question. But on the long run, I think high-quality work will remain visible anyway.
the algo giveth and the algo taketh away. I've been watching physics vids since yt started, and it only chose today to show me this.
sooo perfect this is the bright side of humanity creating and explaining the world !! ( one and only )
This is amazing, please continue making such amazing videos! This surely deserves more watches
I really like this visualization, thank you.
So good. Period. Thank you so much.
Excellent presentation
Fantastic clarity and right on point.. thanks !
This is an extremely useful video! Conceptually, I am trying to visualize how each spherical harmonic can be a superimposition of traveling waves to form the standing wave oscillation on the sphere. For example, I can visualize how in the m=0, l=1 harmonic, this could be visualized in two dimensions as two single wavelength traveling waves originating at the north pole, traveling on opposite sides of a circle and crossing each other at the south pole to return to the the origin, and the average wave intensity would be similar to the oscillation you show with the node at the equator. What seems harder to visualize is how real traveling waves could form the m=1, l=2 scenario where the nodal lines are perpendicular on the sphere. I read for example that this might be like circularly polarized traveling waves on the sphere with the 90 degree rotated components of the waves accounting for the two 90 degree separated nodal lines, although I am struggling to determine if that is the correct way to visualize it or if it is actually due to some other pattern of traveling waves. Any chance you could comment on the correct way to visualize the m=1, l=2 as traveling waves?
Just plug in the equations. This is what I did. Good luck!
So this is where quantum numbers come from…. Finally makes sense
Waah, the best 👍
Wow just amazing so this is what math looks like
this is awesome!
This is the best explanation. thank you !
It's a truly amazing video!
Finally someone explained why orbitals looks like those weird shaped blobs!!❤
Great video, but in the end, why are only the m=0 spheres pulsating and all the other ones are just rotating without any deformation?
In the video, I show the real part of Y_lm exp(i w t), which either has a cos(+|m| \phi + w t) (right moving) or cos( - |m| \phi + w t) (left moving) term, which leads in the time dependence to the "rotating bubble" without further deformation, since time only appears in this term. Thanks for the question!
Thank you so much this is amazingly helpful
Thank you. This truly helped me alot. Thank you
What a representation!! Wonderful.
I started thinking about this after watching a singer shatter a wine glass by singing at it using its resonant frequency. Putting more energy into it than it could handle. A bit like a photon escaping. Then I considered how the glass could flex, and how physical limitations would cause any oscillation that wasn't at a resonant frequency to be self canceling, since the ends of the oscillation wouldn't meet. Then I imagined the limitations in 3 dimensions and how with something as small as an atom, unaffected by the macro universe, there would be basically no damping, so this "wine glass" could ring virtually forever.
Thanks for this great video. Which software do you use for creating the visualization?
It deserves billion likes ,♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
I like that, thank you!
This is awesome. The semi-circle transformation kinda confused me. I thought it was sliding at first, but looking at one quadrant shows it to be streching and shrinking
We just used the mathematical expressions for the spherical harmonics- and this is what we get.
Thank you for pointing this out 😭😭 I was so lost
good catch. This is why mass distributions don't have a "dipole moment"--it's just a translation of the center-of-mass.
also, since z is arbitrary, can you figure out which combinations of of m = +/- 1 are shifts in the x and y directions? (Hint: ask chemist).
While spherical harmonics are the eigenfunctions of the hydrogen atom to describe its state, which are the eigenfunctions for the other 117 chemical elements (helium, etc.)?
Thank you so much!!
Very impressive video..
Beautiful....🙏thank you so much...
Fantastic
Thanks for the clear and concise conceptual explanation! Additionally, when somebody can't fit into their favourite pair of jeans anymore, we could say "you're looking a bit too 2nd spherical harmonic for those". :D
it depends on the phase (prolate or oblate). Note that the L=2 harmonics of a shape *are* it's moment-of-inertia tensor, so it captures both your weight and, wait for it, "how your body carries the weight").
@@DrDeuteron Haha cool! Yeah I learnt just enough about it to implement for diffuse global illumination from an environment map, but one day I'll circle back and try to understand it fully. :)
@@leighkite1164 another comment points out the similarity to Fourier series, where you project an arbitrary function onto pure sine and cosine functions,-standard in so many field. It really is the same thing, just on a sphere instead of a string or a plane.
Have fun with it.
See "Wigner d-Matrix" for a deep dive.
Vid : Harmonics go burr...
My Brain : Ha ha Squishy Squoshy Bloby Bloby lol
Fascinating
thank you so much!
For those That prefer a mechanical analog you can look at harmonics of a guitar string and such.
The video I present is another mechanical method of quantizing a system. It is one of two methods where structures can actually be produced.
th-cam.com/video/wrBsqiE0vG4/w-d-xo.htmlsi=waT8lY2iX-wJdjO3
Area under a curve is often equivalent to energy.
Buckling of an otherwise flat field shows a very rapid growth of this area. If my model applies, it may show how the universe’s energy naturally developed from the inherent behavior of fields.
Under the right conditions, the quantization of a field is easily produced.
The ground state energy is induced via Euler’s contain column analysis.
Containing the column must come in to play before over buckling, or the effect will not work.
The sheet of elastic material “system” response in a quantized manor when force is applied in the perpendicular direction.
Bonding at the points of highest probabilities and maximum duration( ie peeks and troughs) of the fields “sheet” produced a stable structure when the undulations are bonded to a flat sheet that is placed above and below the core material.
There is no need for a mechanical analog. Spherical harmonics are just harmonics of 3d pressure waves in any fluid. You can create those shapes with sound. A loudspeaker is a dipole in the air medium, and this creates waves who's shape is the first harmonic, because the presence of one low and high pressure point is what polarity is. The 2 pressure zones have a spherical influence, and this creates the motion of a pulsating sphere where high and low pressure areas alternate, creating the shape of the first harmonic.
The reason this also happens with atoms is because the universe too is a mechanical fluid. Fluid dynamics alone creates all there is. Electrical charge is just mechanical pressure inside the fluid that is space, and fluid motion of any kind produces toroidal force fields, regardless of it being water, air or space, I which case they are simply labeled as magnetic fields.
Is there a connections between civil engineered trusses and atomic structures?
This video shows a natural quantized effect using a version Euler’s Contain Column Theory?
This video of an engineering test models the quantum physics problem called “Particle in a Box”. The wave function is used to predict the location of quantum particles, atomic structure and molecules.
th-cam.com/video/wrBsqiE0vG4/w-d-xo.htmlsi=J5jCMxq3pRe_P-gG
Very stable trusses and truss core panels have been fabricated using the process shown in the video.
The video shows how materials naturally respond to induced stresses in a “quantized“ manor.
The process’s load/deflection’s sawtooth curve with its exponential fit in the engineering study shows the previously unknown bifurcation between quantum jumps.
The effect has been used to make light weight structures and shock mitigating/recoiled reduction systems and earthquakes isolation systems.
The model shows why with the, exponential load increase and loss of resistance at phase change, quantum jumps are so very fast.
The question whether Laplace had thought of them like this and how he had visualized them ?
A genius like Laplace just used the equations, I believe.
thank you
I have never used the following phrase before, but I think here it is quite fitting. What the actual fuck!?
Finally THANKSS ALOTTTT
What is the software used to make these videos?
Do you have research for dynamical behaviour of the earth? Do see oval shapes in objects in space so ...they perhaps can be round/sphere on another time frame. (perhaps in thousand years). Do see a lot of static anal;yses of the earth and also mostly local. Do not see many global analyses of the earth and its shape for instance ....volume changes in relation to volcansim. Earthquakes and how they move along the earth and insde the earth.
Great...!
Watching your video, I was able to find the surface equation of l=0,1,2.... for m=0 but not for all values m, how can I get that ?
here. www.quantumreflections.net/subdimension-line-u2/spherical-vibrations/spherical-harmonics/
thanks much
amazing
Awesome
So there are 2l+1 modes of vibration but which one we call the first overtone, second overtone, and so on.
PLEASE HELP
We have 2l+1 modes with l nodal lines in TWO dimensions (surface of a sphere). Overtones are related to vibrations of a string in ONE dimension. The groud tone is given by l=1, the first overtone l=2, etc. See
www.quantumreflections.net/subdimension-line-u2/standing-waves/spectrum-of-a-guitar-string/
@@quantumvisionsumunster8208
Ohh thank you!!
see "Chladni Plates" for a 2D generalization .
I have never seen the nodal analysis before, and I thought I'd seen *everything* about Y_lm.
More general: www.quantenspiegelungen.de/en/subdimension-line-u3/topology-of-the-quantum-dimension/ see also my technical comments on www.quantenspiegelungen.de/wp-content/uploads/QuantumVisions.pdf (starts at p. 89)
@@quantumvisionsumunster8208 very cool. My German is pretty bad, even after spending 5 years at DESY.
rotating the nodal lines was a bit hard to follow visually, thus conceptually, but great content.
i studied mindlin plate theory at uni last year, i wonder if these shapes are dictated by the boundary conditions. i just know this is going to be a rabbit hole for me 😂
Just look into you textbook. Indeed, spherical harmonics give a complete basis on the sphere. Not much choice left. Generalization to spin is shown here: www.quantenspiegelungen.de/en/subdimension-line-u3/topology-of-the-quantum-dimension/topology-and-quantum-nodes/
Am I the only one who couldn't get anything in the first watch.??
boy if that doesnt look like orbitals
are you /sarc-ing? If not: they don't just look them, they *are* them!
that's what orbitals are. And btw, the language and interpretation of modern physics is false. Atoms are just those spherical harmonics in a premarital fluid that is the fabric of space , there are no electrons, protons or anything like that. They are are just mathematical artifacts and forcefully upheld as concepts, but completely obsolete and not real. They are just the number of low pressure and high pressure areas of the magnetic fields who's vibration produces the orbital shapes
The spherical harmonics are 3d dimensional em waves which are produced by a bunch of equal magnetic fields sticking together. If you take a magnet and draw a line perpendicular to its field lines, you get the shape of the first harmonic. if you take another one of equal size and strength and let it stick together, you get the second harmonic and so on.
Sound waves make the exact same shape, a dipole make the first harmonic.
Finally, the whole universe is just a fluid in motion. You can simulate the entire universe just with fluid mechanics by postulating a fluid that is modelled as being composed of a single particle with Planck's length as it's radius, and 0 properties except radius and density. The fluid has an internal pressure and seeks pressure equilibrium. It also has no friction or 0 viscosity.
Electrical charge is just a local pressure that is lower or higher than the equilibrium or the medium.
Fluids form toroidal force fields when their balance is disturbed. If you push any volume of fluid, the density of it's destination is increased because you push more fluid into a volume where there already is just the amount of fluid to be in equilibrium, so that area then becomes higher pressure or density. The old location of the displaced volume of fluid leaves a void behind, which is low pressure. The fluid is filling the void left behind, so from all around the void except from the direction you push it in, fluid rushes towards the center of the void. The opposite happens to the high pressure zone, fluid flows away in all directions except from where it came from. In a 3d fluid simulation, the fluid motion traces out a toroidal force field. That is what a magnetic field is.
The point is that the universe itself is just a fluid, and fluid mechanics alone creates everything there is. The 100s of hypothetical particles of mainstream physics are just specific force signature of specific subatomic interactions which of course is why they are quantized. But they are not matter, just forces.
Matter is exclusively made up of magnetic fields, and the number of electrons and protons just corresponds to the number of fields that make up the atoms. Electricity is not electrons flowing, it's fluid flow who's energy is a multiple of the one that is mapped to the electron, but what's flowing is not actually matter, it's just fluid who's kinetic energy was previously part of the movement that produces the harmonics.
@@sshreddderr9409 thank you
It's an atom
Holy fuck.
This loos like some Hollywood movie.
Thanks a lot... in contrast to Hollywood, we just want to teach physics. Not more and not less.
Bernier Shoals