An Extension of Many-Interacting-Worlds Method on Non-Guassian Model

TL;DR

This paper extends the many-interacting-worlds method to non-Gaussian quantum systems, specifically the one-dimensional Coulomb potential, providing theoretical convergence proof and numerical validation consistent with standard quantum mechanics.

Contribution

The paper introduces an extension of the many-interacting-worlds method to Coulomb potentials and proves its convergence, broadening its applicability to non-Gaussian quantum systems.

Findings

Successful extension to Coulomb potential

Convergence of density function proved

Numerical results align with standard quantum mechanics

Abstract

Discussions about whether quantum theory is determinism or indeterminism has lasted for a century. A new approach to standard quantum mechanics called many-interacting-worlds method based on many-worlds interpretation and de Broglie-Bohm mechanics provided the possibility to demonstrate probability from deterministic universe.The many-interacting-worlds method has been proved successful in the ground state of harmonic oscillator. In this article we extend this method to one dimensional Coulomb potential and construct a corresponding empirical density function. We also provide a theoretical proof of the convergence of density function. Our numerical simulation of one dimensional Coulomb potential in the first excited state obtains the consistent result with standard quantum mechanics and shows the applicability of many-interacting-worlds method. This research provides the possibility to extend many-interacting-worlds method to non-Gaussian quantum systems.