Exact solution for particle trajectories in modified quantum mechanics

V.E. Mitroshin

Exact solutions of several nonstationary problems of quantum mechanics are obtained. It is shown that if the initial conditions of the problem correspond to the localized-in-space particle, then it moves exactly along the classical trajectory, and the wave packet is not spread in time.

Anastasios Kyprianidis

Ángel S. Sanz, Salvador Miret-Artés

Vladislav G. Bagrov, Владимир Владимирович Белов, I. M. Ternov

In this paper we show that for a nonrelativistic charged particle moving in an arbitrary external electromagnetic field there exist approximate solutions of the Schrödinger equation, such that the quantum-mechanical averages of the coordinates and the momenta with respect to these states are general exact solutions of the classical Hamiltonian equations. Such states are called trajectory-coherent states. The wave functions of the trajectory-coherent states are obtained by the complex germ method by V. P. Maslov. The simplest properties of these states are studied.

A. Orefice, Raffaele Giovanelli, Domenico Ditto

We present here the exact, trajectory based wave-mechanical description of particle dynamics provided by the time-independent Schroedinger equation, of which the time-dependent equation allows a statistical treatment. Let us remind, for comparison, that Bohmian mechanics is largely recognized to provide a basically hydrodynamic formulation of the quantum theory, describing the evolution of physical systems in terms of statistical streamlines which indicate the regions of space where the moving particles preferentially gather: the very concept of true particle path is avoided, in Bohmian theory, by a weak, non-perturbing measurement. In the present paper the wave-dynamical Hamiltonian equations providing the exact particle trajectories are directly obtained from the time-independent Schroedinger equation, and numerical solutions are presented for a number of different external potentials acting on the moving particles. A Wave-Potential function (holding for any - even classical - wave process described by a Helmholtz-like equation) is shown to be the one and only cause of wave-like features such as diffraction and interference, and to act, for matter waves, without any wave-particle energy exchange.

Shinil Cho