Related papers: Interference in Bohmian Mechanics with Complex Act…
In recent years there has been a resurgence of interest in Bohmian mechanics as a numerical tool because of its local dynamics, which suggest the possibility of significant computational advantages for the simulation of large quantum…
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 present a unified derivation of Bohmian methods that serves as a common starting point for the derivative propagation method (DPM), Bohmian mechanics with complex action (BOMCA) and the zero-velocity complex action method (ZEVCA). The…
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…
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…
David Bohm shown that the Schr{\"o}dinger equation, that is a "visiting card" of quantum mechanics, can be decomposed onto two equations for real functions - action and probability density. The first equation is the Hamilton-Jacobi (HJ)…
Bohmian mechanics, widely known within the field of the quantum foundations, has been a quite useful resource for computational and interpretive purposes in a wide variety of practical problems. Here, it is used to establish a comparative…
This chapter provides a comprehensive overview of the Bohmian formulation of quantum mechanics. It starts with a historical review of the difficulties found by Louis de Broglie, David Bohm, and John S. Bell to convince the scientific…
Bohmian mechanics is an interpretation of quantum mechanics that describes the motion of quantum particles with an ensemble of deterministic trajectories. Several attempts have been made to utilize Bohmian trajectories as a computational…
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…
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…
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…
We generalize the de Broglie-Bohm (dBB) formulation of quantum mechanics to the case of quantum gravity (QG) by using the effective action for a QG theory. This is done by replacing the dBB equations of motion with the effective action…
The exact factorization of an electron-nuclear wavefunction [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)] allows us to define the rigorous nuclear time-dependent Schr\"{o}dinger equation (TDSE) with a…
We describe the advantages and disadvantages of numerical methods when Bohmian trajectory-grids are used for numerical simulations of quantum dynamics. We focus on the crucial non crossing property of Bohmian trajectories, which numerically…
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:…
Since its inception Bohmian mechanics has been generally regarded as a hidden-variable theory aimed at providing an objective description of quantum phenomena. To date, this rather narrow conception of Bohm's proposal has caused it more…
We present a novel perspective on gravity-induced wave function reduction using Bohmian trajectories. This study examines the quantum motion of both point particles and objects, identifying critical parameters for the transition from…
Recently, Bohmian mechanics has been challenged [Nature 643, 67 (2025)] by studying a system in which the motion of particles cannot be associated only with the gradient of phase of the wave function. We point out that, in general, Bohmian…
Perhaps because of the popularity that trajectory-based methodologies have always had in Chemistry and the important role they have played, Bohmian mechanics has been increasingly accepted within this community, particularly in those areas…