Eigenstates in the Many Interacting Worlds Approach: Focus on 2D Ground States

The Many-Interacting-Worlds (MIW) approach to a quantum theory without wave functions proposed in [8] leads naturally to numerical integrators of the Schrödinger equation on comoving grids. As yet, little is known about concrete MIW models for more than one spatial dimension and/or more than one particle. In honour of Detlef Dürr, we report on a further development of the MIW approach to treat arbitrary degrees of freedom and provide a numerical proof of concept for ground states in 2d. The latter is part of a systematic numerical study [22] that includes also 1d ground and excited states. With this step towards the treatment of higher degrees of freedom we hope to stimulate their further study.