ℓ-oscillators from second-order invariant PDEs of the centrally extended conformal Galilei algebras

@article{Aizawa2015oscillatorsFS,
  title={ℓ-oscillators from second-order invariant PDEs of the centrally extended conformal Galilei algebras},
  author={Naruhiko Aizawa and Zhanna Kuznetsova and Francesco Toppan},
  journal={Journal of Mathematical Physics},
  year={2015},
  volume={56},
  pages={031701}
}
We construct, for any given l=12+N0, the second-order, linear partial differential equations (PDEs) which are invariant under the centrally extended conformal Galilei algebra. At the given l, two invariant equations in one time and l+12 space coordinates are obtained. The first equation possesses a continuum spectrum and generalizes the free Schrodinger equation (recovered for l=12) in 1 + 1 dimension. The second equation (the “l-oscillator”) possesses a discrete, positive spectrum. It… 
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