# From Free Motion on a 3-Sphere to the Zernike System of Wavefronts Inside a Circular Pupil

@article{Wolf2020FromFM, title={From Free Motion on a 3-Sphere to the Zernike System of Wavefronts Inside a Circular Pupil}, author={Kurt Bernardo Wolf}, journal={Journal of Physics: Conference Series}, year={2020}, volume={1540} }

Classical or quantum systems that stem from a basic symmetry are seen to be special in having several important properties. The harmonic oscillator and the Bohr system are such. Recent research into the Zernike system provides reasons to include it in this privileged class. Here we show that free motion on the 3-sphere can be projected down to produce classical orbits or complete and orthogonal bases for wavefronts in a circular pupil. This line of inquiry has been pursued in company with N.M…

## 2 Citations

### Higher-order superintegrable momentum-dependent Hamiltonians on curved spaces from the classical Zernike system

- Mathematics, PhysicsNonlinearity
- 2023

We consider the classical momentum- or velocity-dependent two-dimensional Hamiltonian given by where q i and p i are generic canonical variables, γ n are arbitrary coefficients, and N∈N . For N = 2,…

### On the generalization of classical Zernike system

- Mathematics
- 2022

We generalize the results obtained recently (Nonlinearity 36 (2023), 1143) by providing a very simple proof of the superintegrability of the Hamiltonian H = ~p 2 + F ( ~q · ~p ), ~q, ~p ∈ R 2 , for…

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