Related papers: Floydian trajectories for stationary systems: a mo…
It is often argued that measurable predictions of Bohmian mechanics cannot be distinguished from those of a theory with arbitrarily modified particle velocities satisfying the same equivariance equation. By considering the wave function of…
Quantum hydrodynamics is a formulation of quantum mechanics based on the probability density and flux (current) density of a quantum system. It can be used to define trajectories which allow for a particle-based interpretation of quantum…
Bohmian trajectories have been used for various purposes, including the numerical simulation of the time-dependent Schroedinger equation and the visualization of time-dependent wave functions. We review the purpose they were invented for:…
Bohmian mechanics is a non-relativistic quantum theory based on a particle approach. In this paper we study the Schr\"odinger equation with rapidly oscillating potential and the associated Bohmian trajectory. We prove that the corresponding…
The Bohmian interpretation of quantum mechanics adds particle trajectories to the wave function and ensures that the probability distribution of the particle positions agrees with quantum mechanics at any time. This is not sufficient to…
Bohmian mechanics is a deterministic theory of quantum mechanics that is based on a set of n velocity functions for n particles, where these functions depend on the wavefunction from the n-body time-dependent Schroedinger equation. It is…
With an apparent delay of over one century with respect to the development of standard Analytical Mechanics, but still in fully classical terms, the behavior of classical monochromatic wave beams in stationary media is shown to be ruled by…
The path integral approach to quantum mechanics requires a substantial generalisation to describe the dynamics of systems confined to bounded domains. Non-local boundary conditions can be introduced in Feynman's approach by means of…
We present the stochastic Schroedinger equation for the dynamics of a quantum particle coupled to a high temperature environment and apply it the dynamics of a driven, damped, nonlinear quantum oscillator. Apart from an initial slip on the…
Complexified Lienard-Wiechert potentials simplify the mathematics of Kerr-Newman particles. Here we constrain them by fiat to move along Bohmian trajectories to see if anything interesting occurs, as their equations of motion are not known.…
We consider the problem of whether there are deterministic theories describing the evolution of an individual physical system in terms of the definite trajectories of its constituent particles and which stay in the same relation to Quantum…
The generic Bohmian trajectories are calculated for an isolated particle in an approximate energy eigenstate, for an arbitrary one-dimensional potential well. It is shown, that the necessary and sufficient condition for there to be a…
We propose new equations of motion under the theory of the Brownian motion to connect the states of quantum, diffusion, soliton, and periodic localization. The new equations are nothing but the classical equations of motion with two…
Discussion of the differences between the trajectory representation of Floyd and that of Bouda and Djama [Phys. Lett. A 285 (2001) 27, quant-ph/0103071] renders insight: while Floyd's trajectories are related to group velocities, Bouda and…
The dynamical behavior of interacting systems plays a fundamental role for determining quantum correlations, such as entanglement. In this Letter, we describe temporal quantum effects of the inseparable evolution of composite quantum states…
This paper presents a new approach to phase space trajectories in quantum mechanics. A Moyal description of quantum theory is used, where observables and states are treated as classical functions on a classical phase space. A quantum…
We propose an approximate solution of the time-dependent Schr\"odinger equation using the method of stationary states combined with a variational matrix method for finding the energies and eigenstates. We illustrate the effectiveness of the…
We discuss quantum dynamics in multi-dimensional non-linear systems. It is well-known that wave functions are localized in a kicked rotor model. However, coupling with other degrees of freedom breaks the localization. In order to clarify…
Consider a linear autonomous Hamiltonian system with a time periodic bound state solution. In this paper we study the structural instability of this bound state ^M relative to time almost periodic perturbations which are small, localized…
A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method [10]. This quantum model is then associated with a stochastic…