On the self-interference in electron scattering: Copenhagen, Bohmian and geometrical interpretations of quantum mechanics

TL;DR

This paper compares Copenhagen, Bohmian, and geometrical interpretations of quantum mechanics in explaining electron self-interference, proposing a geometrical approach that unifies wave and particle aspects without wavefunction collapse.

Contribution

It introduces a geometrical formulation of quantum mechanics that incorporates wave effects into phase space, offering an alternative deterministic interpretation.

Findings

All three interpretations successfully describe electron scattering and interference.

The geometrical approach aligns with quantum measurements without wavefunction collapse.

The paper demonstrates the equivalence and differences of the interpretations in specific scattering scenarios.

Abstract

Self-interference embodies the essence of the particle-wave interpretation of quantum mechanics (QM). According to the Copenhagen particle-wave interpretation of QM, self-interference by a double slit requires a large transverse coherence of the incident wavepacket such that it covers the separation between the slits. Bohmian dynamics provides a first step in the separation of the particle-wave character of particles by introducing deterministic trajectories guided by a pilot wave that follows the time-dependent Schr\"odinger equation. In this work, I present a theory for quantum dynamics that incorporates all quantum (wave) effects into the geometry of the underlying phase space. This geometrical formulation of QM is consistent with quantum measurements and provides an alternative interpretation of quantum mechanics in terms of deterministic trajectories. In particular, it removes the need for the concept of wavefunction collapse (of the Copenhagen interpretation) to explain the emergence of the classical world. All three QM formulations (Schr\"odinger, Bohmian, and geometrical) are applied to the description of the scattering of a free electron by a hydrogen atom and a double slit.