Quantum Mechanics and Hidden Superconformal Symmetry

Understand

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 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 wavefunction parity.