The scars are then the effect of the wave beat between those various oscillatory components that leads to the probability amplification along the classical periodic trajectory.

For instance, I found this phenomenon called "scarring," where quantum waves bear definite "scars" of classical trajectories, by doing artistic rendering of data.

Contributions from paths wildly different from the classical trajectory may be suppressed by interference (see below).

Semiclassical methods such as periodic-orbit theory connecting the classical trajectories of the dynamical system with quantum features.

In the classical limit, quantum characteristics reduce to classical trajectories.

According to the Feynman scheme, classical trajectories correspond to quantum pathways possessing minimal action.

For an elliptical arena, the scarring is particularly pronounced at the foci, as this is the region where many classical trajectories converge.

In general, modes of a waveguide have "scars", which correspond to the classical trajectories.

Further, contrary to the energy eigenstates of the system, the time evolution of a coherent state is concentrated along the classical trajectories.

But in 1744 Maupertuis had shown that classical trajectories are just these paths of stationary action.