The 1-dimensional quantum form of this system has Hermite polynomials for eigenfunctions and one can use ladder operators to find that the ground state energy is the reduced Planck's constant times angular frequency.
The 3-dimensional isotropic quantum version of this system can be used to model electrons in a metal and has eigenfunctions involving the Laguerre polynomials. The 1-dimensional quantum form of this system has Hermite polynomials for eigenfunctions and one can use ladder operators to find that the ground state energy is the reduced Planck's constant times angular frequency. The classical version of this system is often compared to an (*) RLC electrical circuit and the Q factor relates the damping constant to the frequency. Solutions to them feature sinusoidal motion and, in the simplest case, their potential energy is proportional to one half times the displacement squared. For 10 points, name this type of system that obeys Hooke's law, exemplified by pendulums and masses on springs, which are referred to as the "simple" type.
The 3-dimensional isotropic quantum version of this system can be used to model electrons in a metal and has eigenfunctions involving the Laguerre polynomials.
harmonic oscillator [accept quantum harmonic oscillator; accept simple harmonic oscillator; accept QHO; accept SHO; prompt on partial answers]