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Recently the Many-Interacting-Worlds (MIW) approach to a quantum theorywithout wave functions was proposed. This approach leads quite naturally tonumerical integrators of the Schr\"odinger equation. It has been suggested thatsuch integrators may feature advantages over fixed-grid methods for highernumbers of degrees of freedom. However, as yet, little is known about concreteMIW 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 offreedom, and provide a systematic study of a corresponding numericalimplementation for computing one-particle ground and excited states in onedimension, and ground states in two spatial dimensions. With this step towardsthe treatment of higher degrees of freedom we hope to stimulate their furtherstudy.

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