Lagrangian Formulation for Particle Interpretations of Quantum Mechanics: Single-Particle Case

TL;DR

This paper develops a Lagrangian framework for particle-based interpretations of quantum mechanics, exemplified by the Bohm model, ensuring energy-momentum conservation and compatibility with quantum predictions.

Contribution

It introduces a unified Lagrangian formulation that describes both field and particle dynamics in quantum mechanics, specifically applied to the Bohm model.

Findings

Lagrangian density yields both field and particle equations of motion.

Energy and momentum conservation are inherently satisfied.

The formulation aligns with standard quantum mechanical predictions.

Abstract

A Lagrangian description is presented which can be used in conjunction with particle interpretations of quantum mechanics. A special example of such an interpretation is the well-known Bohm model. The Lagrangian density introduced here also contains a potential for guiding the particle. The advantages of this description are that the field equations and the particle equations of motion can both be deduced from a single Lagrangian density expression and that conservation of energy and momentum are assured. After being developed in a general form, this Lagrangian formulation is then applied to the special case of the Bohm model as an example. It is thereby demonstrated that such a Lagrangian description is compatible with the predictions of quantum mechanics.