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This is Lithium, visualized as a quantum wavepacket. The bright structures are 3D isosurfaces of the outer electron’s probability density, while colour represents the complex phase. Unlike Hydrogen, Lithium’s valence electron moves in a screened potential created by the nucleus and the closed 1s² core. The animation solves that... show more

Mathelirium

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176,633 görüntüleme • 1 ay önce •via X (Twitter)

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Tobie Venne profil fotoğrafı

Tobie Venne1 ay önce

Lithium... top tier nucleator.. Why do you think there was over 200kg of it on the MH370 flight....

Larry Panozzo profil fotoğrafı

Larry Panozzo1 ay önce

Reality is wild, and most of it is invisible to us

Pode profil fotoğrafı

Pode1 ay önce

Neat. Now do the nucleus 😜

Janne Särkelä profil fotoğrafı

Janne Särkelä1 ay önce

@DanielleFong The real disturbance in the fo… field

M profil fotoğrafı

M1 ay önce

how much of this visualization is possible from tying down the pde to random timevalues

drdonhen profil fotoğrafı

drdonhen1 ay önce

cf (from first principles):

Mythic: CEO of Gnoticing profil fotoğrafı

Mythic: CEO of Gnoticing1 ay önce

"I know Gravity is Electromagnetic, but I can't prove it yet..."

Stone Kaiju ᯅ ⚡ ³³º¹ profil fotoğrafı

Stone Kaiju ᯅ ⚡ ³³º¹1 ay önce

Trace amounts may be a cure for Alzheimer’s Lithium orate has been used successfully in tests with rats as this form is able to pass through the blood brain barrier. Study Reference: Published in Nature (August 6, 2025) by Dr. Bruce Yankner’s lab at Harvard Medical School (Title: Lithium deficiency drives Alzheimer’s disease pathology and cognitive decline). Key Findings: Mass spectrometry of human post-mortem brains revealed selective early depletion of trace lithium in the prefrontal cortex during MCI. Pathological Aβ plaques act as a physical sink, sequestering free ionic lithium. Mechanism: Lithium depletion disinhibits GSK3β, driving tau phosphorylation, microglial dysfunction, and synaptic loss. Pharmacokinetics: Among 16 tested salts, low-dose lithium orotate bypassed plaque sequestration (unlike lithium carbonate) and restored cognitive function in mouse models at roughly 1/1000th of psychiatric dosages. Clinical Status: Human pilot and biomarker trials (e.g., Johns Hopkins) are currently underway. Patients/family should be advised against OTC self-medication due to unverified human safety dosing, unregulated supplement purity, and potential renal/thyroid monitoring needs.

Chad DiGirolamo profil fotoğrafı

Chad DiGirolamo1 ay önce

No wonder our “science” is jacked

Farmer Skot profil fotoğrafı

Farmer Skot1 ay önce

Incredible work.

stunspot | ⟨🤩⨯📍⟩ | profil fotoğrafı

stunspot | ⟨🤩⨯📍⟩ |1 ay önce

Now: Why the FUCK is there so MUCH of the damned stuff all over the place?!?!

LaserEyeRobot profil fotoğrafı

LaserEyeRobot1 ay önce

I knew it!

N.A. Cottrell profil fotoğrafı

N.A. Cottrell1 ay önce

matter

fFaceCharli and Mr. E present YOUR DOOM, or 4given profil fotoğrafı

fFaceCharli and Mr. E present YOUR DOOM, or 4given1 ay önce

#farout , man.

Astro 🏴 profil fotoğrafı

Astro 🏴1 ay önce

Brother, no need for digital animations of atoms and elementary particles. The ancient hidden mountain tribe “Afareet Al Jibaal” in modern day Iraq/Iran have a custom blend of components that enables directed higher dimensional journeys. But it’s not for the faint of heart 🤣

Pai Mei profil fotoğrafı

Pai Mei1 ay önce

Dude that’s a jawbreaker.

Dale Cloudman profil fotoğrafı

Dale Cloudman1 ay önce

Why does anyone refer to electrons as particles anymore... it is just not a particle.

Mantis Shrimp profil fotoğrafı

Mantis Shrimp1 ay önce

Beyond physical intuition. So weird.

Frankenbyte profil fotoğrafı

Frankenbyte1 ay önce

Really nice!🌟

wuchengying profil fotoğrafı

wuchengying1 ay önce

alive

Jeff profil fotoğrafı

Jeff1 ay önce

115 please 🙂

Avisek kumar profil fotoğrafı

Avisek kumar1 ay önce

Hi , I wanted to know if we can extend this to cluster of atoms to see the quantum fluctuations of the larger body

MathPolice profil fotoğrafı

MathPolice1 ay önce

Stunning and elucidating as usual. Tangentially related:

Mauro profil fotoğrafı

Mauro1 ay önce

Adore the math behind it

CD profil fotoğrafı

CD1 ay önce

Beating like a living organ. Does this mean that matter is alive ?

BROOKLYDAMUS profil fotoğrafı

BROOKLYDAMUS1 ay önce

Closed eye visuals

FaraOne profil fotoğrafı

FaraOne1 ay önce

Amazing!

Dale Cloudman profil fotoğrafı

Dale Cloudman1 ay önce

And they call it 'inert' matter

Jose Angel Solorzano Luna profil fotoğrafı

Jose Angel Solorzano Luna1 ay önce

@grok I love to eat edible lithium lollipops as a quantum wavepacket

Alchemy profil fotoğrafı

Alchemy1 ay önce

Is this real or simulation image @grok ?

winter ❄️ profil fotoğrafı

winter ❄️1 ay önce

boundary conditions

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This is a Rubidium Rydberg wavepacket reshaped by an external electric field. The electron is not shown as a particle. The surface represents regions of high probability density, |Ψ|², while the colours show the quantum phase, arg(Ψ).

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Mathelirium

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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 moving on a fixed path. The yellow sphere at the centre is the proton, not the electron. The colored 3D surface around it shows places where the electron is more likely to be, i.e. a probability cloud.

Mathelirium

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Now, we move on to Sodium, where the quantum geometry becomes even richer. Here, the valence electron is built from a coherent superposition of s, p, and d Rydberg states. Because these three families experience the Sodium core differently, their energies are shifted by different quantum defects. Their phases therefore drift apart and reunite at different rates.

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Quantum Mechanics How an Electron Moves Around an Atom Here, we modelled an electron in a Hydrogen atom using the Schrödinger equation, combining several quantum states to show how its probability cloud changes, spreads, and reforms over time. The glowing cloud shows where the electron is most likely to be found, its colours represent the quantum phase, the faint ring marks the classical orbital scale, and the tiny dot at the centre represents the atom’s nucleus.

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The positron is the antimatter partner of the electron and together they form positronium... a tiny quantum system with no nucleus. We used the time-dependent Schrödinger equation to evolve the electron and positron clouds. Their motion comes from their quantum states changing over time and the color from phase.

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Mathelirium

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There is almost no magnetic field where the electron travels. Yet, the wavefunction still knows the flux is there. This is the Aharonov-Bohm effect. We numerically solved the time-dependent Schrödinger equation with the Aharonov-Bohm vector potential. From the evolving wavefunction, we calculated the probability density and the guage-corrected quantum probability current. Just for aesthetic beauty, we mark probability current as luminous flowing filaments/threads. Probability density is marked by the bright underlying coloured field/cloud.

There is almost no magnetic field where the electron travels. Yet, the wavefunction still knows the flux is there. This is the Aharonov-Bohm effect. We numerically solved the time-dependent Schrödinger equation with the Aharonov-Bohm vector potential. From the evolving wavefunction, we calculated the probability density and the guage-corrected quantum probability current. Just for aesthetic beauty, we mark probability current as luminous flowing filaments/threads. Probability density is marked by the bright underlying coloured field/cloud.

Mathelirium

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Philosophy Of Physics

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A Quantum Current Chooses a Path A single electron enters a microscopic interferometer, but its wavefunction travels through two routes at once. One branch crosses a resonant quantum dot while the other moves freely around a ring threaded by magnetic flux. The probability current is j = (ℏ/m) Im(ψ*∇ψ) - (q/m)A|ψ|², while the enclosed flux creates the Aharonov-Bohm phase Δφᴬᴮ = qΦ/ℏ. The quantum dot adds the resonant phase δ(E) = atan2(Γ, E - E₀), producing Fano interference when the two paths recombine. Wave packets split, become temporarily trapped, form circulating current vortices, reverse direction after a flux quench, and finally escape through the drain in a coherent burst. The glowing threads are material curves transported by v = j/ρ, revealing how invisible quantum phase controls the flow. #QuantumMechanics #AharonovBohmEffect #QuantumInterference #QuantumDot #ProbabilityCurrent #MesoscopicPhysics #PhysicsAnimation #Physics

A Quantum Current Chooses a Path A single electron enters a microscopic interferometer, but its wavefunction travels through two routes at once. One branch crosses a resonant quantum dot while the other moves freely around a ring threaded by magnetic flux. The probability current is j = (ℏ/m) Im(ψ*∇ψ) - (q/m)A|ψ|², while the enclosed flux creates the Aharonov-Bohm phase Δφᴬᴮ = qΦ/ℏ. The quantum dot adds the resonant phase δ(E) = atan2(Γ, E - E₀), producing Fano interference when the two paths recombine. Wave packets split, become temporarily trapped, form circulating current vortices, reverse direction after a flux quench, and finally escape through the drain in a coherent burst. The glowing threads are material curves transported by v = j/ρ, revealing how invisible quantum phase controls the flow. #QuantumMechanics #AharonovBohmEffect #QuantumInterference #QuantumDot #ProbabilityCurrent #MesoscopicPhysics #PhysicsAnimation #Physics

Mathelirium

16,736 görüntüleme • 3 ay önce

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

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

Mathelirium

30,529 görüntüleme • 7 ay önce

Quantum mechanics has a reputation for being mystical mainly because people skip the rules and jump to interpretations. In this lecture series, we’re doing the opposite. We start from the rules, follow the algebra, and let the picture be the calculation. Classical Probability Theory combines alternatives by adding their probabilities. Quantum Theory combines them one step earlier…add complex amplitudes first, then square at the end. That swap in order is everything. Expand |a₁ + a₂|² and you don’t just get |a₁|² + |a₂|²…you get a cross-term, 2 Re(a₁ a₂*). Its sign is set by phase, so the same two contributions can reinforce or cancel. Interference is just the algebra of squaring a sum. In the 3D render, the surface height is proportional to |a(x)| (so peaks become bright bands after squaring), while the surface skin is colored by the local phase arg(a(x)). As the phase knob φ(t) is swept on path 2, the cross-term oscillates, and you literally watch the interference ridges slide across the screen. We model a detector screen with coordinates x in R² (think x = (x,y)). A quantum state assigns a complex amplitude a(x). The rule for outcomes is p(x) = |a(x)|² Now the key situation: two coherent alternatives contribute to the same outcome x. Let their amplitudes be a₁(x) and a₂(x). Quantum says a(x) = a₁(x) + a₂(x) So the probability density becomes p(x) = |a₁(x) + a₂(x)|² Expand it (this is the whole episode): p(x) = (a₁ + a₂)(a₁* + a₂*) = |a₁|² + |a₂|² + a₁ a₂* + a₁* a₂ = |a₁|² + |a₂|² + 2 Re(a₁ a₂*) That last term is the interference term. It can be positive or negative. To see phase explicitly, write each contribution in polar form: a₁(x) = r₁(x) exp(i θ₁(x)) a₂(x) = r₂(x) exp(i θ₂(x)) Then a₁ a₂* = r₁ r₂ exp(i(θ₁ − θ₂)) So the cross-term is 2 Re(a₁ a₂*) = 2 r₁ r₂ cos(θ₁(x) − θ₂(x)) That’s the fringe engine: p(x) = r₁² + r₂² + 2 r₁ r₂ cos(Δθ(x)) Now the phase knob we animate: Add a controllable phase shift φ to path 2: a₂(x) → a₂(x) exp(i φ) Then Δθ(x) → Δθ(x) − φ, so p(x; φ) = r₁² + r₂² + 2 r₁ r₂ cos(Δθ(x) − φ) As φ changes smoothly, the bright/dark pattern slides continuously. Same setup, same geometry, same magnitudes r₁,r₂, only phase changed. #QuantumMechanics #WaveInterference #ComplexAmplitudes #DoubleSlit #Physics #Mathematics

Quantum mechanics has a reputation for being mystical mainly because people skip the rules and jump to interpretations. In this lecture series, we’re doing the opposite. We start from the rules, follow the algebra, and let the picture be the calculation. Classical Probability Theory combines alternatives by adding their probabilities. Quantum Theory combines them one step earlier…add complex amplitudes first, then square at the end. That swap in order is everything. Expand |a₁ + a₂|² and you don’t just get |a₁|² + |a₂|²…you get a cross-term, 2 Re(a₁ a₂). Its sign is set by phase, so the same two contributions can reinforce or cancel. Interference is just the algebra of squaring a sum. In the 3D render, the surface height is proportional to |a(x)| (so peaks become bright bands after squaring), while the surface skin is colored by the local phase arg(a(x)). As the phase knob φ(t) is swept on path 2, the cross-term oscillates, and you literally watch the interference ridges slide across the screen. We model a detector screen with coordinates x in R² (think x = (x,y)). A quantum state assigns a complex amplitude a(x). The rule for outcomes is p(x) = |a(x)|² Now the key situation: two coherent alternatives contribute to the same outcome x. Let their amplitudes be a₁(x) and a₂(x). Quantum says a(x) = a₁(x) + a₂(x) So the probability density becomes p(x) = |a₁(x) + a₂(x)|² Expand it (this is the whole episode): p(x) = (a₁ + a₂)(a₁ + a₂) = |a₁|² + |a₂|² + a₁ a₂ + a₁* a₂ = |a₁|² + |a₂|² + 2 Re(a₁ a₂) That last term is the interference term. It can be positive or negative. To see phase explicitly, write each contribution in polar form: a₁(x) = r₁(x) exp(i θ₁(x)) a₂(x) = r₂(x) exp(i θ₂(x)) Then a₁ a₂ = r₁ r₂ exp(i(θ₁ − θ₂)) So the cross-term is 2 Re(a₁ a₂*) = 2 r₁ r₂ cos(θ₁(x) − θ₂(x)) That’s the fringe engine: p(x) = r₁² + r₂² + 2 r₁ r₂ cos(Δθ(x)) Now the phase knob we animate: Add a controllable phase shift φ to path 2: a₂(x) → a₂(x) exp(i φ) Then Δθ(x) → Δθ(x) − φ, so p(x; φ) = r₁² + r₂² + 2 r₁ r₂ cos(Δθ(x) − φ) As φ changes smoothly, the bright/dark pattern slides continuously. Same setup, same geometry, same magnitudes r₁,r₂, only phase changed. #QuantumMechanics #WaveInterference #ComplexAmplitudes #DoubleSlit #Physics #Mathematics

Mathelirium

81,784 görüntüleme • 10 ay önce

We evolve a complex quantum field ψ(x,y,t) with a Schrödinger-Poisson flow: i ψ_t = -(1/2)Δψ + (V_conf(x,y) + G Φ(x,y,t)) ψ, with ρ=|ψ|² and ΔΦ = ρ - ⟨ρ⟩. That bracket (V_conf + GΦ) is just the potential energy landscape. V_conf is the trap you choose by hand (a smooth bowl that keeps the wave from drifting away). Φ is the field generated by the wave’s own density...compute ρ, solve the Poisson equation, feed Φ back into the evolution. G is the knob that sets how strongly the wave feels its own Φ. Visually Hue is phase φ=arg(ψ), brightness is density ρ^γ, the banded helicoids are phase ribbons cos(mφ+θ(t)), the bright ridges are boosted by |∇ρ|, and the tiny white pearls mark vortices where the phase winding satisfies ∮∇φ·dl = 2πk. #QuantumMechanics #SchrodingerPoisson #ComputationalPhysics #PhysicsVisualization

We evolve a complex quantum field ψ(x,y,t) with a Schrödinger-Poisson flow: i ψ_t = -(1/2)Δψ + (V_conf(x,y) + G Φ(x,y,t)) ψ, with ρ=|ψ|² and ΔΦ = ρ - ⟨ρ⟩. That bracket (V_conf + GΦ) is just the potential energy landscape. V_conf is the trap you choose by hand (a smooth bowl that keeps the wave from drifting away). Φ is the field generated by the wave’s own density...compute ρ, solve the Poisson equation, feed Φ back into the evolution. G is the knob that sets how strongly the wave feels its own Φ. Visually Hue is phase φ=arg(ψ), brightness is density ρ^γ, the banded helicoids are phase ribbons cos(mφ+θ(t)), the bright ridges are boosted by |∇ρ|, and the tiny white pearls mark vortices where the phase winding satisfies ∮∇φ·dl = 2πk. #QuantumMechanics #SchrodingerPoisson #ComputationalPhysics #PhysicsVisualization

Mathelirium

18,700 görüntüleme • 9 ay önce

Why Does Quantum Mechanics Use a Complex Wavefunction? Schrödinger’s equation doesn’t start from mystery. It starts from a very specific bet. The state of a particle is a complex field ψ(x,t), and whatever time-evolution rule we choose has to move ψ forward while preserving total probability. So the basic question is simple. What equation should ψ satisfy so that |ψ|² behaves like a conserved density, the way mass density does in fluid flow? What is ψ? Think of ψ(x,t) as an amplitude attached to the statement the particle is at position x at time t. It’s not a probability. It’s the thing you add first, and only at the end do you square it: p(x,t) = |ψ(x,t)|² Because ψ is complex, it has magnitude and phase. Write it as ψ(x,t) = r(x,t) exp(i θ(x,t)) Then r² = |ψ|² is the density, and the phase θ ends up controlling the flow through the probability current. Where does Schrödinger’s equation come from? Start with two empirical inputs that tie waves to particles: E = ħ ω p = ħ k Here ħ is Planck’s constant divided by 2π. It’s the conversion factor between frequency and energy, and between wavenumber and momentum. A plane wave with angular frequency ω and wavevector k is ψ(x,t) = A exp(i(k·x − ωt)) Now watch what derivatives do to this wave: ∂ψ/∂t = −i ω ψ ∇ψ = i k ψ ∇²ψ = −|k|² ψ Multiply by ħ and you get: i ħ ∂ψ/∂t = ħ ω ψ = E ψ −i ħ ∇ψ = ħ k ψ = p ψ −ħ² ∇²ψ = ħ² |k|² ψ = p² ψ So for plane waves, the operators Ê = i ħ ∂/∂t p̂ = −i ħ ∇ act like energy and momentum. Now bring in the classical, nonrelativistic energy bookkeeping: E = p²/(2m) + V(x) Kinetic plus potential. That’s it. Turn it into an equation for ψ by replacing E and p with the operators above: Ê ψ = (p̂²/(2m) + V) ψ Since p̂² = (−i ħ ∇)·(−i ħ ∇) = −ħ² ∇², this becomes i ħ ∂ψ/∂t = ( −ħ²/(2m) ∇² + V(x) ) ψ That’s the time-dependent Schrödinger equation. This derivation is a controlled heuristic. Match the plane-wave identities to the measured relations E = ħω and p = ħk, then impose the same energy bookkeeping you trust in classical mechanics. Why this is the right kind of rule If ψ is the state, we need a rule that preserves total probability: ∫ |ψ(x,t)|² dx = 1 Schrödinger evolution does, and you can see it by deriving a continuity equation. Let ρ(x,t) = |ψ|² = ψ*ψ. Differentiate: ∂ρ/∂t = ψ* ∂ψ/∂t + ψ ∂ψ*/∂t Use Schrödinger and its complex conjugate. The potential terms cancel, and what’s left can be rearranged into ∂ρ/∂t + ∇·j = 0 with probability current j = (ħ/(2mi)) ( ψ* ∇ψ − ψ ∇ψ* ) That’s the cleanest way to say what ψ is. |ψ|² behaves like a conserved density, the phase drives a current, and the time evolution is fixed, up to V, by combining wave relations with energy bookkeeping: i ħ ∂ψ/∂t = ( −ħ²/(2m) ∇² + V ) ψ #QuantumMechanics #SchrodingerEquation #WaveFunction #BornRule #Physics #MathematicalPhysics

Why Does Quantum Mechanics Use a Complex Wavefunction? Schrödinger’s equation doesn’t start from mystery. It starts from a very specific bet. The state of a particle is a complex field ψ(x,t), and whatever time-evolution rule we choose has to move ψ forward while preserving total probability. So the basic question is simple. What equation should ψ satisfy so that |ψ|² behaves like a conserved density, the way mass density does in fluid flow? What is ψ? Think of ψ(x,t) as an amplitude attached to the statement the particle is at position x at time t. It’s not a probability. It’s the thing you add first, and only at the end do you square it: p(x,t) = |ψ(x,t)|² Because ψ is complex, it has magnitude and phase. Write it as ψ(x,t) = r(x,t) exp(i θ(x,t)) Then r² = |ψ|² is the density, and the phase θ ends up controlling the flow through the probability current. Where does Schrödinger’s equation come from? Start with two empirical inputs that tie waves to particles: E = ħ ω p = ħ k Here ħ is Planck’s constant divided by 2π. It’s the conversion factor between frequency and energy, and between wavenumber and momentum. A plane wave with angular frequency ω and wavevector k is ψ(x,t) = A exp(i(k·x − ωt)) Now watch what derivatives do to this wave: ∂ψ/∂t = −i ω ψ ∇ψ = i k ψ ∇²ψ = −|k|² ψ Multiply by ħ and you get: i ħ ∂ψ/∂t = ħ ω ψ = E ψ −i ħ ∇ψ = ħ k ψ = p ψ −ħ² ∇²ψ = ħ² |k|² ψ = p² ψ So for plane waves, the operators Ê = i ħ ∂/∂t p̂ = −i ħ ∇ act like energy and momentum. Now bring in the classical, nonrelativistic energy bookkeeping: E = p²/(2m) + V(x) Kinetic plus potential. That’s it. Turn it into an equation for ψ by replacing E and p with the operators above: Ê ψ = (p̂²/(2m) + V) ψ Since p̂² = (−i ħ ∇)·(−i ħ ∇) = −ħ² ∇², this becomes i ħ ∂ψ/∂t = ( −ħ²/(2m) ∇² + V(x) ) ψ That’s the time-dependent Schrödinger equation. This derivation is a controlled heuristic. Match the plane-wave identities to the measured relations E = ħω and p = ħk, then impose the same energy bookkeeping you trust in classical mechanics. Why this is the right kind of rule If ψ is the state, we need a rule that preserves total probability: ∫ |ψ(x,t)|² dx = 1 Schrödinger evolution does, and you can see it by deriving a continuity equation. Let ρ(x,t) = |ψ|² = ψψ. Differentiate: ∂ρ/∂t = ψ ∂ψ/∂t + ψ ∂ψ/∂t Use Schrödinger and its complex conjugate. The potential terms cancel, and what’s left can be rearranged into ∂ρ/∂t + ∇·j = 0 with probability current j = (ħ/(2mi)) ( ψ ∇ψ − ψ ∇ψ* ) That’s the cleanest way to say what ψ is. |ψ|² behaves like a conserved density, the phase drives a current, and the time evolution is fixed, up to V, by combining wave relations with energy bookkeeping: i ħ ∂ψ/∂t = ( −ħ²/(2m) ∇² + V ) ψ #QuantumMechanics #SchrodingerEquation #WaveFunction #BornRule #Physics #MathematicalPhysics

Mathelirium

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