Solvability of the ubiquitous quantum harmonic oscillator relies on a spectrum generating osp(1|2) superconformal symmetry. We study the problem of constructing all quantum mechanical models with a hidden osp(1|2) symmetry on a given space of states. This problem stems from interacting higher spin models coupled to gravity. In one dimension, we show that the solution to this problem is the Vasiliev-Plyushchay family of quantum mechanical models with hidden superconformal symmetry obtained by viewing the harmonic oscillator as a one dimensional Dirac system, so that Grassmann parity equals wave function parity. These models - both oscillator and particlelike - realize all possible unitary irreducible representations of osp(1|2).

Quantum mechanics and hidden superconformal symmetry / Bonezzi, R.; Corradini, O.; Latini, E.; Waldron, A.. - In: PHYSICAL REVIEW D. - ISSN 2470-0010. - 96:126005(2017), pp. 1-12.

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