The operator problem of this name can be solved by the so-called "algebraic method" using the raising and lowering operators and was solved by Dirac to model photons. The utility of this model arises 
The operator problem of this name can be solved by the so-called "algebraic method" using the raising and lowering operators and was solved by Dirac to model photons. The utility of this model arises because of the nature of the first-order expansion of a potential energy about an equilibrium. The equation by this name arises from a quadratic-potential Lagrangian or from combining Newton's second law and Hooke's law. This is therefore a good model for a perturbed atom, AC circuit, first-order pendulum, or mass on a spring. FTP, name these physical systems that, if unforced, have sinusoidal motion.
The operator problem of this name can be solved by the so-called "algebraic method" using the raising and lowering operators and was solved by Dirac to model photons.
harmonic oscillators [prompt on oscillators; accept quantum or simple harmonic oscillators]