Related papers: Wave Functions and Bohmian Trajectories in Interfe…
Bohmian mechanics is the most naively obvious embedding imaginable of Schr\"odinger's equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at…
In recent years, intensive effort has gone into developing numerical tools for exact quantum mechanical calculations that are based on Bohmian mechanics. As part of this effort we have recently developed as alternative formulation of…
Bohmian mechanics, a hydrodynamic formulation of the quantum theory, constitutes a useful tool to understand the role of the phase as the mechanism responsible for the dynamical evolution displayed by quantum systems. This role is analyzed…
In ref [1], a criterion has been derived for the objective wave function reduction through the Shr\"odinger-Newton equation. In this paper, we shall derive that criterion by using the concept of Bohmian trajectories. This study has two…
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…
Mermin's "shut up and calculate!" somehow summarizes the most widely accepted view on quantum mechanics. This conception has led to a rather constraining way to think and understand the quantum world. Nonetheless, a closer look at the…
The compatibility of standard and Bohmian quantum mechanics has recently been challenged in the context of two-particle interference, both from a theoretical and an experimental point of view. We analyze different setups proposed and derive…
Bohmian mechanics provides an explanation of quantum phenomena in terms of point particles guided by wave functions. This review focuses on the formalism of non-relativistic Bohmian mechanics, rather than its interpretation. Although the…
The hydrogen atom is a system amenable to an exact treatment within Schroedinger's formulation of quantum mechanics according to coordinates in four systems -- spherical polar, paraboloidal, ellipsoidal and spheroconical coordinates; the…
Hydrodynamics and quantum mechanics have many elements in common, as the density field and velocity fields are common variables that can be constructed in both descriptions. Starting with the Schroedinger equation and the Klein-Gordon for a…
We propose that the Schrodinger equation results from applying the classical wave equation to describe the physical system in which subatomic particles play random motion, thereby leading to quantum mechanics. The physical reality described…
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:…
According to Schroedinger's ideas, classical dynamics of point particles should correspond to the " geometrical optics " limit of a linear wave equation, in the same way as ray optics is the limit of wave optics. It is shown that, using…
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, a hydrodynamic formulation of quantum mechanics, relies on the concept of trajectory, which evolves in time in compliance with dynamical information conveyed by the wave function. Here this appealing idea is considered to…
The Schrodinger equation has been considered to be a postulate of quantum physics, but it is also perceived and derived heuristically as the quantum equivalent of the classical energy relation. We indicate that the Schrodinger equation…
It is shown that the Schrodinger equation for a large family of pairs of two-dimensional quantum potentials possess wavefuctions for which the amplitude and the phase are interchangeable, producing two different solutions which are dual to…
We solve the time-dependent Schr\"odinger equation by learning the score function, the gradient of the log-probability density, on Bohmian trajectories. In Bohm's formulation of quantum mechanics, particles follow deterministic paths under…
Following Ref. [Oriols X 2007 Phys. Rev. Lett., 98 066803], an algorithm to deal with the exchange interaction in non-separable quantum systems is presented. The algorithm can be applied to fermions or bosons and, by construction, it…
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…