The quantum harmonic oscillator as a Zariski geometry

A structure is associated with the quantum harmonic oscillator, over a fixed algebraically closed field FF of characteristic 0, which is shown to be uncountably categorical. An analysis of definable sets is carried out, from which it follows that this structure is a Zariski geometry of dimension 1. It is non-classical in the sense that it is not interpretable in ACF0ACF0 and in the case F=CF=C, is not a structure on a complex manifold.