This article explores a possible physical interpretation of the wavefunction. It zooms in on the physical model it implies for an electron in free space (further building on Schroedinger's ideas in regard to the apparent Zitterbewegung of an electron), but then also discusses the wavefunction for particles (including non-charged particles) in general. While it basically concludes that the mainstream interpretation of quantum physics (the Copenhagen interpretation) is and remains the most parsimonious explanation, it also argues that one or two extra assumptions – the wavefunction as a two-dimensional self-sustaining electromagnetic or gravitational oscillation in space – would make more frivolous explanations (many worlds, pilot wave, etcetera) redundant.