Developments of Bohmian Mechanics

TL;DR

This paper merges Bohmian mechanics with an energy conservation approach to create a unified formalism that describes particle dynamics in all quantum states, including stationary states, by interpreting the quantum potential.

Contribution

It introduces a novel formalism combining Bohmian mechanics with an energy-based approach, enabling particle trajectories in stationary states.

Findings

Provides a unified formalism for all quantum states.

Derives a generalized n-body equation with kinetic and pressure terms.

Extends Madelung equations to include stationary states.

Abstract

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 well know that Bohmian mechanics is not applicable to stationary states, since the velocity field for stationary states is the zero function. Recently, an alternative to Bohmian mechanics has been formulated, based on a conservation of energy equation, where the velocity fields are not the zero function, but this formalism is only applicable to stationary states with real valued wavefunctions. In this paper, Bohmian mechanics is merged with the alternative to Bohmian mechanics. This is accomplished by introducing an interpretation of the Bohm quantum potential. The final formalism gives dynamic particles for all states, including stationary states. The final main working equation contains two kinetic energy terms and a term that contains a factor that can be interpreted as a pressure. The derivation is a simple n-body generalization of the recent generalization, or refinement, of the Madelung equations.