The equation moves amplitudes.
The solver alternates exact phase rotations generated by V(x) and by kinetic energy in Fourier space. No random choices occur during this evolution.
Live numerical state
Equation Lab / Quantum mechanics
Watch ψ evolve.
The Schrödinger equation evolves a complex quantum state deterministically. This lab solves that evolution in real time, then lets you sample positions separately using the Born rule.
03 / Ask a position question
Sample the Born rule.
Each detection is drawn from P(x) = |ψ(x)|². Sampling here does not alter the evolving state; it isolates the probability postulate from the equation of motion.
Detector countsn = 0
Height is not a particle cloud.
The luminous curtain is |ψ|², a probability density for position measurements. Its phase—essential for interference—is encoded by color and the complex-space curve.
The math does not settle ontology.
This demonstration evolves ψ and applies the Born rule. It does not decide whether particles have hidden trajectories, branches split, or collapse is physically fundamental.