Quantum carpet · A3
|ψ(x, t)|²: position up, time across, sampled once per classical period so the bouncing slows to a crawl. The packet smears out (collapse), splits into q copies at T_rev/q, re-forms mirrored at T_rev/2 and whole at T_rev. The line is now.
Wavepacket in the well
The potential, |ψ(x)|² now (same strobe as the carpet) drawn at the packet's energy, and the levels it is made of: bar length = |cₙ|².
Return probability |⟨ψ(0)|ψ(t)⟩|²
1 at the launch; ½ at T_rev/4 and ⅓ at T_rev/3 (two and three copies, one of them back home); 1 again at T_rev. Faint: with pure dephasing.
Spectrum
live output · markers: Bohr frequencies (Eₙ₊ₖ − Eₙ)/hEach Δn = k makes a cluster of lines near k × the note, spaced 2k/T_rev apart: neighbouring lines beat at the revival.
Spectrogram
live output · ticks: the spectrum's markersWatch a note collapse and come back: the lines fade as the packet smears out and return at the revival; in between, fractional revivals bring it back an octave or a twelfth up.