The energy eigenfunctions
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}