Bohmian mechanics: A legitimate hydrodynamic picture for quantum mechanics, and beyond

TL;DR

This paper discusses the evolution of Bohmian mechanics from a controversial hidden-variable theory to a practical computational tool, examining its legitimacy and applications in quantum mechanics and beyond.

Contribution

It provides a historical and conceptual analysis of Bohmian mechanics, highlighting its shift towards operational and computational utility rather than hidden-variable interpretation.

Findings

Bohmian mechanics has gained acceptance as a pragmatic analytical tool.

The Schrödinger equation is re-examined through a less restrictive perspective.

Numerical examples illustrate the practical applications of Bohmian mechanics.

Abstract

Since its inception, Bohmian mechanics has been surrounded by a halo of controversy. Originally proposed to bypass the limitations imposed by von Neumann's theorem on the impossibility of hidden-variable models in quantum mechanics, it faced strong opposition from the outset. Over time, however, its use in tackling specific problems across various branches of physics has led to a gradual shift in attitude, turning the early resistance into a more moderate acceptance. A plausible explanation for this change may be that, since the late 1990s and early 2000s, Bohmian mechanics has been taking on a more operational and practical role. The original hidden-variable idea has gradually faded from its framework, giving way to a more pragmatic approach that treats it as a suitable analytical and computational tool. This discussion explores how and why such a shift in perspective has occurred and, therefore, answers questions such as whether Bohmian mechanics should be considered once and for all a legitimate quantum representation (i.e., worth being taught in elementary quantum mechanics courses) or, by extension, whether these ideas can be transferred to and benefit other fields. Here, the Schr\"odinger equation and several specific numerical examples are re-examined in the light of a less restrictive view than the standard one usually adopted in quantum mechanics.