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

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.

12 pages

References in corpus (2)

• Symmetry and Evolution in Quantum Gravity
• Lagrangian-Only Quantum Theory

Cited by in corpus (5)

• Lagrangian Description for Particle Interpretations of Quantum Mechanics -- Entangled Many-Particle Case
• Revisiting de Broglie's Double-Solution Pilot-Wave Theory with a Lorentz-Covariant Lagrangian Framework
• Is There Really "Retrocausation" in Time-Symmetric Approaches to Quantum Mechanics?
• Energy-momentum tensor for a field and particle in interaction
• Incorporating action and reaction into a particle interpretation for quantum mechanics -- Schrodinger case