in a quantum-mechanical system, the difference between the ground-state energy and the energy that corresponds to the minimum potential energy. Zero-point energy is a consequence of the uncertainty principle (seeUNCERTAINTY PRINCIPLE).

In classical mechanics it was assumed that a particle can exist in a state of minimum potential energy and have zero kinetic energy. In this case the particle is at stable equilibrium and has a minimum energy equal to the potential energy at the equilibrium point. In quantum mechanics the uncertainty principle states that the range of values Δx for the coordinate x of a particle is related to the range of values ΔP for the particle’s momentum P by the expression ΔPΔx ∼ ħ, where ħ is Planck’s constant. As Δ x → 0, the localization of the particle near the potential energy minimum gives a large value for the particle’s mean kinetic energy, since the range of values of the momentum is large, as implied by the expression ΔP∼ħΔx. On the other hand, when Δx ≠ 0, that is, when the degree of the particle’s localization is reduced, the mean potential energy increases because the particle spends considerable time in an area in which the potential energy exceeds the minimum value the ground-state energy of a quantum-mechanical system corresponds to the lowest energy that is permitted by the uncertainty principle.

Zero-point energy is a general property of all coupled systems of microparticles. It is not possible to convert a system into a state that has an energy lower than zero-point energy without changing the system’s structure.