The equation by this name arises from a quadratic-potential Lagrangian or from combining Newton's second law and Hooke's law.
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]