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Zero-Point Energy

The minimum possible energy of a quantum mechanical system, even at absolute zero temperature, due to the Heisenberg uncertainty principle.
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The statement of the theorem

For a single vibrational mode of a diatomic molecule with reduced mass μ\mu and force constant kk, the system is modeled by the harmonic oscillator Hamiltonian H^HO\hat{H}_{HO}: \nH^HO=p^22μ+12kx^2\hat{H}_{HO} = \frac{\hat{p}^2}{2\mu} + \frac{1}{2}k\hat{x}^2\nThe minimum possible energy, or Zero-Point Energy (ZPE), is the ground state eigenvalue (v=0v=0) of this Hamiltonian:\nEZPE=12ℏω=12ℏkμE_{ZPE} = \frac{1}{2} \hbar \omega = \frac{1}{2} \hbar \sqrt{\frac{k}{\mu}}
Source: Wikipedia