Zero-point energy

Zero-point energy is the nonzero ground-state energy left by quantum fluctuations. One harmonic oscillator contributes $\omega /2$ before any regularization or normal-ordering subtraction.

Zero-point motion is the nonzero quantum fluctuation of position and momentum in a system's ground state. For a quantum harmonic oscillator, the ground state has energy $\hslash \omega /2$ and nonzero position and momentum variances even at zero temperature. It does not represent a thermal mixture and need not carry entropy. The large zero-point motion of light helium atoms helps explain why helium can remain a liquid at low pressure even as temperature approaches absolute zero.