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This is a visualization of a Rydberg wavepacket. In simple terms it is a way of showing an electron in a very highly excited quantum state. The Math comes from the Schrödinger equation for hydrogen where the electron is described by a wavefunction rather than as a tiny ball... show more

Mathelirium

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15,845 просмотров • 1 день назад •via X (Twitter)

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This is a simulation of a Hydrogen electron described by a superposition of several highly excited Rydberg states. The superposition forms a localized quantum wavepacket that moves around the atom, spreads, splits, and later reforms as the different energy components return to phase.

This is a simulation of a Hydrogen electron described by a superposition of several highly excited Rydberg states. The superposition forms a localized quantum wavepacket that moves around the atom, spreads, splits, and later reforms as the different energy components return to phase.

Mathelirium

40,251 просмотров • 2 дней назад

A Bonus render of Electron Holography for our Quantum Mechanics Lecture Series. We’re staging a TEM-style electron holography shot as a single 3D scene. A coherent electron wave ψ(x,y,t) enters from the left as a localized packet, gets split by a thin biprism phase wedge, then bends around a central nanoring that stands in for an enclosed magnetic flux. The wave evolves by Schrödinger dynamics, so its intensity ρ=|ψ|² is literally the electron detection probability density, while the probability current j=(1/m)Im(ψ*∇ψ) acts like a conserved flow of that density across the plane. The main surface is a living whose height tracks |ψ| and whose skin color cycles with arg(ψ). On top of it, luminous current ribbons trace streamlines of v=j/(ρ+ε), so you can see how phase gradients steer the flow around the ring and back into interference. High above, a tilted detector/hologram screen shows the off-axis fringe image you’d measure (intensity after mixing with a reference wave), while a porcelain bead marks the centroid ⟨x⟩(t) and flux threads through the ring pulse in sync with the Aharonov-Bohm phase knob φ_AB(t). See our lecture series for details. #QuantumMechanics #ElectronHolography #MathematicalPhysics #Physics

A Bonus render of Electron Holography for our Quantum Mechanics Lecture Series. We’re staging a TEM-style electron holography shot as a single 3D scene. A coherent electron wave ψ(x,y,t) enters from the left as a localized packet, gets split by a thin biprism phase wedge, then bends around a central nanoring that stands in for an enclosed magnetic flux. The wave evolves by Schrödinger dynamics, so its intensity ρ=|ψ|² is literally the electron detection probability density, while the probability current j=(1/m)Im(ψ*∇ψ) acts like a conserved flow of that density across the plane. The main surface is a living whose height tracks |ψ| and whose skin color cycles with arg(ψ). On top of it, luminous current ribbons trace streamlines of v=j/(ρ+ε), so you can see how phase gradients steer the flow around the ring and back into interference. High above, a tilted detector/hologram screen shows the off-axis fringe image you’d measure (intensity after mixing with a reference wave), while a porcelain bead marks the centroid ⟨x⟩(t) and flux threads through the ring pulse in sync with the Aharonov-Bohm phase knob φ_AB(t). See our lecture series for details. #QuantumMechanics #ElectronHolography #MathematicalPhysics #Physics

Mathelirium

14,252 просмотров • 7 месяцев назад

Erwin Schrödinger’s 1926 equation changed the game by turning Quantum Mechanics into wave dynamics. That move gave Physics a new way to think. Instead of forcing a particle onto one sharp path, it lets a complex wavefunction evolve in time, with its shape and phase holding the structure of the phenomenon. What makes this so striking is that Schrödinger’s equation does not start from vague mystery. It starts from a precise and daring idea The state of a particle is a complex field ψ(x,t), and the dynamics must push ψ forward in a way that preserves total probability.

Erwin Schrödinger’s 1926 equation changed the game by turning Quantum Mechanics into wave dynamics. That move gave Physics a new way to think. Instead of forcing a particle onto one sharp path, it lets a complex wavefunction evolve in time, with its shape and phase holding the structure of the phenomenon. What makes this so striking is that Schrödinger’s equation does not start from vague mystery. It starts from a precise and daring idea The state of a particle is a complex field ψ(x,t), and the dynamics must push ψ forward in a way that preserves total probability.

Mathelirium

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Watch hydrogen atom wavefunctions smoothly transition between quantum states (n,l,m) This is the actual probability density of finding the electron; not just static orbitals, but the real quantum dance as it morphs between energy levels.

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Mathematica

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An Electron flies above a metal grating without touching it. As the electron passes, each groove scatters its electromagnetic near field at a slightly different time. The emissions interfere and produce what's called Smith-Purcell radiation. This effect is being explored for tunable Terahertz radiation, biomedical spectroscopy, and high-speed communications.

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This is Quantum Chaos inside a Bunimovich stadium. The motion is governed by the Schrödinger equation. The whirlpools in the flow are Quantum phase vortices.

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Mathelirium

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Claude and I got a live sodium atom simulation! lightcell energy 🔆 I've long wanted to be able to visualize what is really happening when a neutral sodium atom is excited in a flame or a bulb. Classical theory teaches that the single outer electron orbits the nucleus and full shells, and forms a dipole when this gets "wanged" but, physicists have long wondered, what does it look like when the electron gets wanged? is it like ringing a bell? i thought that this was the perfect time to really push what is capable of, in terms of building artifacts. grabbed zig to compile wasm and webgpu to make it super performant, and work with it for a bit and ran the REAL TIME-DEPENDENT Schrödinger equation on a 3D grid in a potential in the browser. and you can kick it! what!! it's soo beautiful... this is going on the website overhaul for sure here is the artifact. i don't endorse that it's exactly right, but i feel it is probably spiritually a good sodium simulation. it certainly rings my dipole!

Claude and I got a live sodium atom simulation! lightcell energy 🔆 I've long wanted to be able to visualize what is really happening when a neutral sodium atom is excited in a flame or a bulb. Classical theory teaches that the single outer electron orbits the nucleus and full shells, and forms a dipole when this gets "wanged" but, physicists have long wondered, what does it look like when the electron gets wanged? is it like ringing a bell? i thought that this was the perfect time to really push what is capable of, in terms of building artifacts. grabbed zig to compile wasm and webgpu to make it super performant, and work with it for a bit and ran the REAL TIME-DEPENDENT Schrödinger equation on a 3D grid in a potential in the browser. and you can kick it! what!! it's soo beautiful... this is going on the website overhaul for sure here is the artifact. i don't endorse that it's exactly right, but i feel it is probably spiritually a good sodium simulation. it certainly rings my dipole!

Danielle Fong 🔆

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I have not drank a single drop of water in almost 1 year. This is because your body produces its own water as a byproduct of glycolysis. Another anti aging byproduct of glycolysis is the production of NAD+ & NaDH. No electron moves in the body unless it is coupled to hydrogen. Where is the hydrogen in your meat? Don't worry l'll wait. Gary brecka let's run some tests I'm in SoFlo 🙏🏼🙌🏼💯

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Nine years ago today, we launched Electron for the first time. Later this year, Electron is expected to reach 100 launches, likely making it the fastest privately developed orbital rocket to hit that milestone. From “It’s a test” to one of the world’s highest cadence launch vehicles in under a decade. Here's a little walk down memory lane from that first historic launch.

Nine years ago today, we launched Electron for the first time. Later this year, Electron is expected to reach 100 launches, likely making it the fastest privately developed orbital rocket to hit that milestone. From “It’s a test” to one of the world’s highest cadence launch vehicles in under a decade. Here's a little walk down memory lane from that first historic launch.

Rocket Lab

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Phase Space Is the Real Stage of Dynamics. So, Stop Watching the Object and Watch the State. Ordinary Space tells you where something is. Phase Space tells you what state it is in. Position alone is not enough because you also need the variable that tells you where the system is trying to go. In the animation, the left panel shows the particle moving in Ordinary Space, while the right panel shows the same system as a moving point in Phase Space. For one degree of freedom, the state is (x, p) and as time evolves, that state traces a trajectory t ↦ (x(t), p(t)) Instead of thinking of a differential equation as just a formula, Phase Space lets you see it as a flow on the space of states. For this lecture we use ẋ = p ṗ = x − x³ with Hamiltonian H(x,p) = 0.5 p² + 0.25 x⁴ − 0.5 x² #PhaseSpace #DynamicalSystems #NonlinearDynamics #HamiltonianMechanics #Mathematics

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Mathelirium

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$RKLB won the AWS company of the year. Peter Beck highlights: - Electron was the 3rd most rocket launches in the world LAST year. - Electron is the 2nd most rocket-launched in the world THIS year. - Escapade mission 2 spacecrafts just whip passed the moon and are about 1.5 million miles away from Mars and will arrive in Mars' orbit in 1 year. - By then, 20% of what is in Mars' orbit will be built by Rocket Lab "We had a great 2025 , but man, 2026 is going to be way bigger" What a company !!!

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Parkash Heerani

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Is an electron a particle or a wave?⁠ ⁠ In this conversation, physicist Sean Carroll explores some of the deepest mysteries in quantum mechanics: the famous double-slit experiment, wave function collapse, the Many Worlds interpretation, entropy and the arrow of time. ⁠ Watch the full interview here:

Is an electron a particle or a wave?⁠ ⁠ In this conversation, physicist Sean Carroll explores some of the deepest mysteries in quantum mechanics: the famous double-slit experiment, wave function collapse, the Many Worlds interpretation, entropy and the arrow of time. ⁠ Watch the full interview here:

New Scientist

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Quantum Probability Surface Goes Negative A Schrödinger-Cat state is built from two separated coherent wavepackets, |ψ⟩=N(|α⟩+|−α⟩), and its Wigner function reveals the part of Quantum Mechanics that ordinary probability cannot show. The two bright lobes behave like classical possibilities, while the interference between them carves negative valleys into phase space, where W(x,p)<0. In this animation, the surface height is the signed Wigner function. So, gold rises above zero, cyan sinks below it, and the blades between them expose the nonclassical structure of the wavefunction. #QuantumMechanics #WignerFunction #SchrodingerCat #Physics #QuantumArt #ScienceVisualization

Quantum Probability Surface Goes Negative A Schrödinger-Cat state is built from two separated coherent wavepackets, |ψ⟩=N(|α⟩+|−α⟩), and its Wigner function reveals the part of Quantum Mechanics that ordinary probability cannot show. The two bright lobes behave like classical possibilities, while the interference between them carves negative valleys into phase space, where W(x,p)<0. In this animation, the surface height is the signed Wigner function. So, gold rises above zero, cyan sinks below it, and the blades between them expose the nonclassical structure of the wavefunction. #QuantumMechanics #WignerFunction #SchrodingerCat #Physics #QuantumArt #ScienceVisualization

Mathelirium

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In Calculus of Variations, we give up the idea of only optimizing values and start optimizing geometries instead. The unknown is not a single x. It is a whole curve/surface y(x). The object you are minimizing is usually not a simple formula that you can guess. It is an integral that judges the whole shape. In our first lecture, we discuss the famous Brachistochrone problem. You choose two points, turn on gravity and ask a question which almost sounds too simple...which track will allow a bead to move from A to B in the minimum time? At your first attempt, your instinct will lead you astray. It is not the straight line. It is not the drop hard then cruise sketch either. The winner turns out to be a cycloid...the curve a point on a rolling circle traces. The track is the moving character in the animation. We begin with a flawed curve, perform gradient descent in curve-space, and observe the geometry change frame by frame as T[y] collapses to the brachistochrone. Please see the comment below for the math breakdown. #CalculusOfVariations #Brachistochrone #Cycloid #Physics #Optimization #Mathematics

In Calculus of Variations, we give up the idea of only optimizing values and start optimizing geometries instead. The unknown is not a single x. It is a whole curve/surface y(x). The object you are minimizing is usually not a simple formula that you can guess. It is an integral that judges the whole shape. In our first lecture, we discuss the famous Brachistochrone problem. You choose two points, turn on gravity and ask a question which almost sounds too simple...which track will allow a bead to move from A to B in the minimum time? At your first attempt, your instinct will lead you astray. It is not the straight line. It is not the drop hard then cruise sketch either. The winner turns out to be a cycloid...the curve a point on a rolling circle traces. The track is the moving character in the animation. We begin with a flawed curve, perform gradient descent in curve-space, and observe the geometry change frame by frame as T[y] collapses to the brachistochrone. Please see the comment below for the math breakdown. #CalculusOfVariations #Brachistochrone #Cycloid #Physics #Optimization #Mathematics

Mathelirium

23,254 просмотров • 2 месяцев назад

In the heart of every atom, the electron doesn’t glide; it vanishes. Dr. Theresa Bullard on the quantum leap: that “gap” between orbitals isn’t empty. It’s the portal. The electron dissolves into the field of pure potential, then reappears elsewhere. No path. No travel. Just pure becoming. We chase the particles, the light, the matter… but the cosmos is whispering through the silence between. The emptiness that holds everything. This is the quiet engine of reality itself.

In the heart of every atom, the electron doesn’t glide; it vanishes. Dr. Theresa Bullard on the quantum leap: that “gap” between orbitals isn’t empty. It’s the portal. The electron dissolves into the field of pure potential, then reappears elsewhere. No path. No travel. Just pure becoming. We chase the particles, the light, the matter… but the cosmos is whispering through the silence between. The emptiness that holds everything. This is the quiet engine of reality itself.

Cosmos Archive

86,381 просмотров • 4 месяцев назад

What does a hydrogen atom’s |ψ|² actually look like as the quantum numbers change? This animation shows the electron probability density morphing in real time through superpositions α|nlm⟩ + β|n′l′m′⟩ while n, l, and m shift between allowed values.

What does a hydrogen atom’s |ψ|² actually look like as the quantum numbers change? This animation shows the electron probability density morphing in real time through superpositions α|nlm⟩ + β|n′l′m′⟩ while n, l, and m shift between allowed values.

Matheorems

10,305 просмотров • 21 дней назад

The Probability Density of a Brownian Particle Solves the. Heat Equation. Einstein’s 1905 paper on Brownian motion doesn’t get the same spotlight as General Relativity, but it’s still an astonishing piece of work. It takes a messy, noisy phenomenon and extracts three hard facts from it: First, the randomness of the particles is physical. The motion is molecular impacts made visible. Second, one path looks like chaos, but the cloud has a rigid scaling law...mean-square displacement grows like t, so the width grows like √t. Third, the cloud evolves deterministically. Its density solves the heat equation PDE! So Brownian probability spreads the same way heat spreads!

The Probability Density of a Brownian Particle Solves the. Heat Equation. Einstein’s 1905 paper on Brownian motion doesn’t get the same spotlight as General Relativity, but it’s still an astonishing piece of work. It takes a messy, noisy phenomenon and extracts three hard facts from it: First, the randomness of the particles is physical. The motion is molecular impacts made visible. Second, one path looks like chaos, but the cloud has a rigid scaling law...mean-square displacement grows like t, so the width grows like √t. Third, the cloud evolves deterministically. Its density solves the heat equation PDE! So Brownian probability spreads the same way heat spreads!

Mathelirium

21,543 просмотров • 5 месяцев назад