Abstract
It is well known that for some equations of motion there exist inequivalent Hamiltonian/Lagrangian structures. This is the so-called inverse problem in variational calculus [1]. It is also well known that these alternative structures yield different quantum theories [2, 3, 4, 5, 6]. In this work we present a continuum of Hamiltonian structures for the two-dimensional isotropic harmonic oscillator; in particular, a continuum of Hamiltonian structures with noncommutative coordinates. We also perform a study of their symmetries.
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