Quantum Harmonic Oscillator
The quantum mechanical analogue of a classical harmonic oscillator, describing a particle bound in a parabolic potential well V(x) = ½ m ω² x².
Governing formula
E_n = (n + ½) ℏ ω, n = 0, 1, 2, 3...
SI unit
eV or Joules
In depth
Energy levels are equally spaced by ℏω. Unlike the classical oscillator, the quantum harmonic oscillator possesses a non-zero ground state zero-point energy E₀ = ½ ℏω at absolute zero.
Examples in the real world
Modeling molecular vibrational spectra and lattice vibrations (phonons) in solid state crystal structures.