Quantum Shock Wave Discontinuities in the Dispersion of Free Gaussian Wave Packets

Katsunori Mita

Oussama Bindech, Roberto R. Marquardt

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.

Helmut Kaiser, S. A. Werner, R. Clothier +2 more

Cathleen A. Brenner, Orville L. Brill

The effects of discontinuities in the zeroth and first derivatives of the Schrödinger wavefunction upon the momentum distribution of a particle are illustrated for the chopped wave state. Smoothing the discontinuities in the chopped wave state by use of a modulated Gaussian results in a single continuous, differentiable wavefunction which, in the corresponding limits, permits proper mathematical treatment of the uncertainty in momentum for four common cases: the chopped wave, the free particle, the Gaussian packet, and the localized particle.

David J. Coughtrie