Quantum Mechanics Without Wavefunctions

TL;DR

This paper introduces a wavefunction-free formulation of quantum mechanics using real-valued trajectories, offering new perspectives on quantum states that could impact theory, computation, and interpretation.

Contribution

It develops a self-contained, wavefunction-free approach to quantum mechanics based on real trajectories, applicable to any configuration space and system dimensionality.

Findings

Provides a trajectory-based representation of quantum states

Discusses benefits for theory, computation, and interpretation

Applicable to arbitrary configuration spaces

Abstract

We present a self-contained formulation of spin-free nonrelativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories, obtained by extremizing an action and satisfying energy conservation. The theory applies for arbitrary configuration spaces and system dimensionalities. Various beneficial ramifications - theoretical, computational, and interpretational - are discussed.