Simulations of quantum wavefunctions evolving in selected potentials answers the question: Is there a quantum trajectory? See the companion blog at galileo-unboun... that discusses quantum chaos in terms of nonlinear physics and chaos theory. Surprisingly, quantum trajectories share much in common with classical trajectories, especially for the harmonic oscillator. This video includes a 2D harmonic oscillator, a 2D double-well potential (with a time-reversal operation that creates a wavefunction echo) and the 2D Henon-Heiles potential (a system that displays classical chaos).
The 2D harmonic oscillator simulation uses an initial condition of two wave packets on opposite sides, either stationary, or else orbiting the origin. The Henon-Heiles simulation uses an initial stationary wave packet at the origin, or two packets in motion. The double-well simulation uses a stationary wave packet that accelerates towards the opposite well, or two stationary wave packets that "fall into" the potential wells.
The simulations are based on FDTD (Finite-Difference Time-Domain) solutions to the Schrödinger equation. Initial conditions are taken as Gaussian wave packets that are either stationary or moving.
26 сен 2024
