An N=8 supersymmetric mechanics with potential is built on rigid special Kähler manifolds, yielding bosonic Hamiltonians that include superintegrable deformations of the 2D oscillator and Coulomb problem.
A note on quantum Bohlin transformation
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abstract
It is shown, that the reduction of the circular quantum oscillator by the $Z_2$-group action results to the two systems: a two-dimensional hydrogen atom, and a ``charge - charged magnetic vortex" one, with the spin $\frac 12$. Analogously, the $Z_N$-reduction of the two-dimensional system with the central potential $r^{2(N-1)}$ results into $N$ bound ``charge - magnetic vertex" systems with the interaction potential $r^{2(1/N-1)}$ and spins $\sigma=\frac kN$, $k =0,1,..., (N-1)$.
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Geometry and integrability in $\mathcal{N}=8$ supersymmetric mechanics
An N=8 supersymmetric mechanics with potential is built on rigid special Kähler manifolds, yielding bosonic Hamiltonians that include superintegrable deformations of the 2D oscillator and Coulomb problem.