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Self-interference embodies the essence of the particle-wave interpretation ofquantum mechanics (QM). According to the Copenhagen particle-waveinterpretation of QM, self-interference by a double slit requires a largetransverse coherence of the incident wavepacket such that it covers theseparation between the slits. Bohmian dynamics provides a first step in theseparation of the particle-wave character of particles by introducingdeterministic trajectories guided by a pilot wave that follows thetime-dependent Schr\"odinger equation. In this work, I present a theory forquantum dynamics that incorporates all quantum (wave) effects into the geometryof the underlying phase space. This geometrical formulation of QM is consistentwith quantum measurements and provides an alternative interpretation of quantummechanics in terms of deterministic trajectories. In particular, it removes theneed for the concept of wavefunction collapse (of the Copenhageninterpretation) to explain the emergence of the classical world. All three QMformulations (Schr\"odinger, Bohmian, and geometrical) are applied to thedescription of the scattering of a free electron by a hydrogen atom and adouble slit.

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