= Zero-point energy
{wiki}
Zero-point energy is the <ground-state energy> remaining in a quantum degree of freedom relative to a specified classical energy reference. For the <quantum harmonic oscillator> with potential minimum chosen as zero,
$$
E_0=\frac12\hbar\omega.
$$
Both the <position> and <momentum> spreads remain nonzero. Squeezing one spread increases the other contribution, and their minimum total <energy> is fixed by the <Heisenberg uncertainty principle>.
This energy remains as <temperature> approaches zero; it is not thermal excitation and does not contribute an oscillator heat capacity by itself. In a field theory, summing zero-point terms over infinitely many modes requires a prescription. Changing a nongravitational energy reference does not change transition frequencies, while boundary-dependent energy differences and gravitational coupling require a more careful treatment, as discussed under <vacuum energy>.
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