Wave Packets, Potentials, and Forces

Lyudvig Dmitrievich Faddeev, O. Yakubovskiĭ

S. M. Blinder

Stefano Longhi, S. A. R. Horsley, Giuseppe Della Valle

Wave-packet scattering from a stationary potential is significantly modified when the wave packet is subject to an external time-dependent force during the interaction. In the semiclassical limit, wave-packet motion is simply described by Newtonian equations, and the external force can, for example, cancel the potential force, making a potential barrier transparent. Here we consider wave-packet scattering from reflectionless potentials, where in general the potential becomes reflective when probed by an accelerated wave packet. In the particular case of the recently introduced class of complex Kramers-Kronig potentials we show that a broad class of time-dependent forces can be applied without inducing any scattering, while there is a breakdown of the reflectionless property when there is a broadband distribution of initial particle momentum, involving both positive and negative components.

Babur M. Mirza

In quantum theory particles are represented as wave packets.Shock wave analysis of quantum equations of motion shows that wave function representation in general and wave packet description in particular contain discontinuities due to a non-zero quantum force corresponding to quantum potential.The quantum force causes wave packet dispersion which results in the intersection of characteristic curves developing a shock discontinuity.Since quantum force vanishes for localized quantum density waves [1], it is thus established that localized quantum density waves form the only class of continuous wave representation of particles in quantum theory.

Roderich Tumulka

Giulio Armando Ottonello