Time evolution of wave packets on nanostructures

Time evolution of wave packets on nanostructures is studied on the basis of a three-dimensional solvable model with singular interactions (de Prunele 1997 J. Phys. A: Math. Gen. 30 7831). In particular, methods and tools are provided to determine time independent upper bounds for the overlap of the normalized time-dependent wave packet with the time independent normalized wave packet concentrated at an arbitrarily chosen vertex of the nanosystem. The set of upper bounds referring to all initial positions of the wave packet and all overlaps are summarized in a matrix. The analytical formulation allows a detailed study for arbitrary geometrical configurations. Time evolution on truncated quasicrystalline systems has been found to be site selective, depending on the position of the initial wave packet