New Trajectory Interpretation of Quantum Mechanics

Jochen Pade

Dennis Manuel Heim

Initial momenta of de Broglie-Bohm trajectories generally do not obey quantum mechanical momentum distributions. The solution to this problem presented in the following leads to an extended hydrodynamic interpretation of quantum mechanics. To demonstrate the new formalism, it is applied to the double-slit experiment. From this example follows a proposal for experimental verification of trajectory formulations of quantum mechanics.

Gregg S. Jaeger

James Paul Wesley

Following de Broglie, Bohm, and others, it is assumed that quantum mechanics may be interpreted causally and that the $\ensuremath{\psi}$ function plays the role of a generating function for particle trajectories. By arguing that the $\ensuremath{\psi}$ function should not be interpreted as a probability amplitude, a new method for generating particle trajectories is postulated. The four-momentum of a scalar particle is assumed to be given as the gradient of an unspecified function $F(\ensuremath{\psi})$, where $\ensuremath{\psi}$ is a pure real solution of the Klein-Gordon equation. Since the location of a particle is determined solely by its trajectory, the probability distribution differs from $\ensuremath{\psi}{\ensuremath{\psi}}^{*}$; and therefore, ordinary experimental results differing from the traditional theory may, in principle, be predicted. Particle motion and trajectories are discussed for three examples: a free particle, a particle in a box, and the double slit.

M. R. Brown

The Floydian trajectory method of quantum mechanics and the appearance of microstates of the Schrödinger equation are reviewed and contrasted with the Bohm interpretation of quantum mechanics. The kinematic equation of Floydian trajectories is analysed in detail and a new definition of the variational derivative of kinetic energy with respect to total energy is proposed for which Floydian trajectories have an explicit time dependence with a frequency equal to the beat frequency between adjacent pairs of energy eigenstates in the case of bound systems. In the case of unbound systems, Floydian and Bohmian trajectories are found to be related by a local transformation of time which is determined by the quantum potential.

Daniel M. Greenberger, Klaus Hentschel, Friedel Weinert