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The semiclassical method is characterized by finite forces and smooth, well-behaved trajectories, but also by multivalued representational functions that are ill-behaved at turning points. In contrast, quantum trajectory methods--based on…
In this review we deal with open (dissipative and stochastic) quantum systems within the Bohmian mechanics framework which has the advantage to provide a clear picture of quantum phenomena in terms of trajectories, originally in…
In the last few years the hydrodynamic formulation of quantum mechanics, equivalent to the Bohmian equations of motion, has been used to obtain numerical solutions of the Schrodinger equation. Problems, however, have been experienced near…
We give a partial review of what is known so far on stability of periodically driven quantum systems versus regularity of the bounded driven force. In particular we emphasize the fact that unbounded degeneracies of the unperturbed…
Trajectory-based approaches to quantum mechanics include the de Broglie-Bohm interpretation and Nelson's stochastic interpretation. It is shown that the usual route to establishing the validity of such interpretations, via a decomposition…
The classical dynamics of a particle that is driven by a rapidly oscillating potential (with frequency $\omega$) is studied. The motion is separated into a slow part and a fast part that oscillates around the slow part. The motion of the…
A solution $\psi $ to Schr\"odinger's equation needs some degree of regularity in order to allow the construction of a Bohmian mechanics from the integral curves of the velocity field $\hbar \Im \left( \bigtriangledown \psi /m\psi \right)…
Diffraction in time of a particle confined in a box which its walls are removed suddenly at $t=0$ is studied. The solution of the time-dependent Schr\"{o}dinger equation is discussed analytically and numerically for various initial…
In this study, we use the concept of Bohmian trajectories to present a dynamical and deterministic interpretation for the gravity induced wave function reduction. We shall classify all possible regimes for the motion of a particle, based on…
A quantum fractal is a wavefunction with a real and an imaginary part continuous everywhere, but differentiable nowhere. This lack of differentiability has been used as an argument to deny the general validity of Bohmian mechanics (and…
Both Bohmian mechanics, a version of quantum mechanics with trajectories, and Feynman's path integral formalism have something to do with particle paths in space and time. The question thus arises how the two ideas relate to each other. In…
Bohmian mechanics is a nonlocal hidden-variable interpretation of quantum theory which predicts that particles follow deterministic trajectories in spacetime. Historically, the study of Bohmian trajectories has mainly been restricted to…
Quantum polarization is investigated by means of a trajectory picture based on the Bohmian formulation of quantum mechanics. Relevant examples of classical-like two-mode field states are thus examined, namely Glauber and SU(2) coherent…
The violation of Bell type inequalities in quantum systems manifests that quantum states cannot be described by classical probability distributions. Yet, Bohmian mechanics is a realistic, non-local theory of classical particle trajectories…
The path integral approach to the quantization of one degree-of-freedom Newtonian particles is considered within the discrete time-slicing approach, as in Feynman's original development. In the time-slicing approximation the quantum…
We present a new variational method for investigating the ground state and out of equilibrium dynamics of quantum many-body bosonic and fermionic systems. Our approach is based on constructing variational wavefunctions which extend Gaussian…
The question of the representation of quantum stationary partially polarized waves as random superpositions of different polarization ellipses is addressed. To this end, the Bohmian formulation of quantum mechanics is considered and…
We present a theoretical method to generate a highly accurate {\em time-independent} Hamiltonian governing the finite-time behavior of a time-periodic system. The method exploits infinitesimal unitary transformation steps, from which…
We explain the approximate nature of particle trajectories in Bohm's quantum mechanics. They are streamlines of a superfluid in Madelung's reformulation of the Schr\"{o}dinger wave function, around which the proper particle trajectories…
Experiments violating Bell's inequality appear to indicate deterministic models do not correspond to a realistic theory of quantum mechanics. The theory of pilot waves seemingly overcomes this hurdle via nonlocality and statistical…