Overview of Bohmian Mechanics

TL;DR

This chapter offers a comprehensive, didactic overview of Bohmian mechanics, covering its history, formalism, measurement process, and computational methods, demonstrating its consistency with standard quantum mechanics and its potential research applications.

Contribution

It provides a detailed, self-contained summary and formal explanation of Bohmian mechanics, including computational algorithms, for both newcomers and researchers.

Findings

Bohmian mechanics reproduces standard quantum correlations.

It offers an ontological, measurement-interaction-based interpretation.

Computational algorithms for Bohmian trajectories are detailed.

Abstract

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 community about the validity and utility of Bohmian mechanics. Then, a formal explanation of Bohmian mechanics for nonrelativistic, single-particle quantum systems is presented. The generalization to many-particle systems, where the exchange interaction and the spin play an important role, is also presented. After that, the measurement process in Bohmian mechanics is discussed. It is emphasized that Bohmian mechanics exactly reproduces the mean value and temporal and spatial correlations obtained from the standard, that is the Copenhagen or orthodox, formulation. The ontological characteristics of Bohmian mechanics provide a description of measurements as another type of interaction without the need for introducing the wave function collapse. Several solved problems are presented at the end of the chapter, giving additional mathematical support to some particular issues. A detailed description of computational algorithms to obtain Bohmian trajectories from the numerical solution of the Schrodinger or the Hamilton-Jacobi equations are presented in an appendix. The motivation of this chapter is twofold: first, as a didactic introduction to Bohmian formalism, which is used in the subsequent chapters, and second, as a self-contained summary for any newcomer interested in using Bohmian mechanics in his or her daily research activity.