2017
DOI: 10.1063/1.4990794
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Quantum superintegrable Zernike system

Abstract: We consider the differential equation that Zernike proposed to classify aberrations of wavefronts in a circular pupil, whose value at the boundary can be nonzero. On this account the quantum Zernike system, where that differential equation is seen as a Schrödinger equation with a potential, is special in that it has a potential and boundary condition that are not standard in quantum mechanics. We project the disk on a half-sphere and there we find that, in addition to polar coordinates, this system separates i… Show more

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Cited by 13 publications
(31 citation statements)
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“…after which, we find that {F 5 , F 6 } = 4F 8 . In this way we build a 10−dimensional Poisson algebra.…”
Section: Adding More Potentials: Super-integrabilitymentioning
confidence: 80%
See 3 more Smart Citations
“…after which, we find that {F 5 , F 6 } = 4F 8 . In this way we build a 10−dimensional Poisson algebra.…”
Section: Adding More Potentials: Super-integrabilitymentioning
confidence: 80%
“…Section 4 is concerned with the classical and quantum Zernike system, whose super-integrability (and much more!) was recently studied in detail by Pogosyan, et al [7,8]. My purpose here is show how the methods of Section 3 can be applied, giving a new perspective on their results.…”
Section: Introductionmentioning
confidence: 93%
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“…[16]), or a Schrödinger equation with a non-standard quantum Hamiltonian H = − 1 2 Z, as done in Ref. [17]. In this paper we shall address the expansions between the original Zernike eigenbasis (labelled I) and two of the new separated eigenbases reported in [17] (labelled II and III).…”
Section: Introductionmentioning
confidence: 98%