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EphemeraWAVEFUNCTION
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A sister instrument to Ephemera

WAVEFUNCTION

Real quantum mechanics. Proven live in your browser.

i·ℏ ∂ψ/∂t = H ψ  ·  |ψₖ|² = the sound

Shape a potential. The wavefunction evolves through it - spreading, ringing, tunneling - and the spectrum is a true probability. Then you observe, and the Born rule collapses it into the sound.

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SchrödingerBorn ruleLindbladAndersonedge modes

Free in browser · every claim re-derived live at /proof

Timbre that obeys the Schrödinger equation.

i·ℏ ∂ψ/∂t = H ψ

Wavefunction is a real quantum synthesizer. Its timbre is a complex wavefunction ψ spread over a bank of partials, evolving unitarily under a Hamiltonian you shape - not a recording of physics, the physics itself, running live.

You don't draw the spectrum. You draw the landscape the wave moves through, and the spectrum is whatever probability the wave settles into. The bright partials are simply where ψ has amplitude.

Nothing is faked. The same engine that makes the sound passes 30+ falsifiable checks live in your browser - the Schrödinger evolution, the Born rule, Lindblad decoherence, Anderson localization, topological edge modes.

The board

Draw a landscape. The wave fills it. Observe, and it collapses to one.

H ψₙ = Eₙ ψₙ  ·  |ψₖ|² = P(k)

One potential holds the whole instrument. The wavefunction settles into the shape you draw - and where it has amplitude is exactly what you hear.

A double-well potential and its wavefunctionA diagram of position along the bottom. A violet double-well potential V of x has two valleys with a barrier between them. An aurora-green band shows the probability density, the absolute value of psi squared, sitting in both wells at once with a thin bridge of amplitude leaking through the barrier - that bridge is quantum tunneling. A violet spike at the right well shows observation: the Born rule collapses the spread-out wave onto a single outcome, and that collapse is the sound.Eₙtunneling - leaks through the barrierobserve → one outcomex - position / mode →↑ V, |ψ|²well - one pitchbarrierwell - another pitchtwo wells, and the wave is in both at once - until you observe.
  • V(x) - the landscape you shape
  • |ψₖ|² - probability = the spectrum
  • observe - the Born rule picks one

How it works

Three moves. One wavefunction.

01

Shape a potential

V(k)

Draw the landscape - flat, a single well, two wells, or disorder. That potential is the only thing you set; it decides how the wave is allowed to move.

02

The wavefunction evolves

i·ℏ ∂ψ/∂t = H ψ

Press a key and ψ evolves through your landscape - spreading, ringing into standing harmonics, tunneling between wells. The spectrum is alive and physically true, not a stored sample.

03

Observe

|ψₖ|² → grain

Measure it. The Born rule collapses the spread-out probability onto a single outcome - the coherent whole becomes a granular click. That collapse is the sound.

Landscapes

Four potentials. Four sounds.

The potential is the only thing you draw - and it decides everything. Each shape is a different corner of real physics, and a different instrument.

Flat

V = 0 · free particle

No potential at all. The packet just spreads - a quantum walk that drifts wider and brighter the longer it runs. The raw material: pure dispersion.

Single well

½k·x² · standing modes

One bowl. The wave settles into clean standing harmonics - a bright, pitched, scale-locked pad. This is the harmonic heart of the instrument.

Double well

two wells · tunnels

Two bowls, a barrier between. The wave is in both at once and slowly sloshes through the wall - audible tunneling that pitch-slides on its own, no LFO drawn.

Disorder

random V · localizes

A jagged, random landscape. The wave can't spread - it freezes into a fixed speckle, trapped in place. Anderson localization you can hear as frozen, grainy texture.

Sound systems

Six ways the wave becomes sound.

Once it's moving, the engine gives you the real toolbox of quantum dynamics - and every one of them is something you can hear.

Coherent ⇌ Lottery

|ψₖ|² → grain

Hear the wave whole as one evolving tone, or flip to Lottery and let the Born rule measure it - each draw fires a grain at one mode. The same physics, two ways to listen.

Decoherence

Lindblad γ

Let the world leak in. Dial γ and the pristine peaks blur toward a thermal floor - or run it as a trajectory and hear each quantum jump as an audible click.

Spinor voices

σ·B → L/R

Give the wave a spin and a magnetic field. It Larmor-precesses, and the up/down components map to left/right - the precession reads as a clean stereo rock you can hear.

Solitons

Gross - Pitaevskii g

Turn on self-attraction and the wave becomes its own well. A struck packet gathers into a breathing soliton that holds its shape - a fat, self-sustaining lead that won't disperse.

Floquet drive

V(t) · Bessel comb

Shake the potential in time and every partial shatters into a Bessel-weighted sideband comb - a metallic shimmer at f ± n·f_d that no static filter or AM/FM can reach.

Polyphony

multi-packet ψ

Play a chord and each held note gets its own wavefunction in its own re-centred well - so chords stay glassy and distinct instead of smearing into one cloud.

Presets

Start from a sound.

Each is a finished voice of the engine - a different landscape and a different physics. Open one in the instrument and reshape it from there.

More presets - spinors, solitons, Floquet combs, topological plateaus - wait inside the instrument.

Proof

Every claim, proven live in your browser.

Most “quantum” audio is a metaphor. This isn’t. The engine that makes the sound is the engine that passes the tests - and you can try to break it.

Try it first, own it later

One instrument, three doors.

Free Web

$0

The full wavefunction in your browser. Shape a landscape, observe, and share by link. No install, no account.

Launch in browser →

Desktop

$19.99

Native app. Offline. A higher-resolution mode engine, audio + MIDI export, CC-routable observables, lifetime updates.

Get the desktop app →

Ephemera Bundle

Included

Wavefunction ships free with Ephemera Premium, a sister instrument to Poles inside the same studio.

See Ephemera →

One-time purchase · no subscriptions, ever · free forever in the browser

“A spectrum is just a probability— and now you can hear it.”

The Wavefunction idea

FAQ

Questions, answered.

No. Draw a landscape, press a key, and listen. That's the whole loop. The Schrödinger equation and the |ψ|² labels are there if you're curious, but you never have to read them to make a sound.

Observe it yourself.

shape · evolve · observe

Free in your browser, no account. Draw a landscape, let the wavefunction find its shape, and measure it. Then open the instrument and take it further.

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