The quantum harmonic oscillator as a Zariski geometry

Vinesh Solanki*, Dmitry Sustretov, Boris Zilber

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

3 Citations (Scopus)


A structure is associated with the quantum harmonic oscillator, over a fixed algebraically closed field IF 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 ACF(0) and in the case F = C, is not a structure on a complex manifold. (C) 2014 Published by Elsevier B.V.

Original languageEnglish
Pages (from-to)1149-1168
Number of pages20
JournalAnnals of Pure and Applied Logic
Issue number6
Publication statusPublished - Jun 2014


  • Interpretability
  • Zariski geometries


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