Eigenstates in the Many Interacting Worlds approach: Ground states in 1D and 2D and excited states in 1D (long version)

TL;DR

This paper advances the Many-Interacting-Worlds approach to quantum mechanics by developing models for multiple degrees of freedom and numerically computing ground and excited states in 1D and 2D, aiming to enhance understanding of higher-dimensional quantum systems.

Contribution

It extends the MIW approach to arbitrary degrees of freedom and provides a systematic numerical study for computing quantum states in higher dimensions.

Findings

Successfully computed one-particle ground and excited states in 1D.

Computed ground states in 2D.

Demonstrated the feasibility of MIW models for higher dimensions.

Abstract

Recently the Many-Interacting-Worlds (MIW) approach to a quantum theory without wave functions was proposed. This approach leads quite naturally to numerical integrators of the Schr\"odinger equation. It has been suggested that such integrators may feature advantages over fixed-grid methods for higher numbers of degrees of freedom. However, as yet, little is known about concrete MIW models for more than one spatial dimension and/or more than one particle. In this work we develop the MIW approach further to treat arbitrary degrees of freedom, and provide a systematic study of a corresponding numerical implementation for computing one-particle ground and excited states in one dimension, and ground states in two spatial dimensions. With this step towards the treatment of higher degrees of freedom we hope to stimulate their further study.