Finite models of the oscillator

摘要

Finite oscillator models obey the same dynamics as classical and quantum oscillators, but these operators, which correspond to position, momentum, Hamiltonian, and angular momentum, are generators of the compact Lie group SO(D) and form the Lie algebra so(D). One-dimensional finite oscillators, shallow planar optical waveguides, and finite data sets are so(3) systems. Two-dimensional finite oscillators, shallow cylindrical waveguides, and pixellated screens are governed by so(4). A physical reinterpretation of the generators of these algebras as observables that take a finite number of values fits into a coherent picture of their phase space.