Classically, the system is described by a second order differential equation that yields sinusoidal solutions unless damping is present.
The energy eigenfunctions of this system are proportional to the Hermite polynomials, while the energy eigenvalues are proportional to h-bar times the angular frequency. One of the most interesting systems that can be solved exactly in quantum mechanics, it can be used to model a variety of physical systems including molecular bonds. Classically, the system is described by a second order differential equation that yields sinusoidal solutions unless damping is present. For ten points, this describes what physical system whose canonical example is a mass on a spring?
The energy eigenfunctions of this system are proportional to the Hermite polynomials, while the energy eigenvalues are proportional to h-bar times the angular frequency.
{harmonic oscillator}