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Quantum harmonic oscillator
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Energy levels are equally spaced.
E_n = (n+½)ħωA quantum oscillator has equally spaced energy levels E_n = (n + ½)ħω and a non-zero ground-state energy. It models phonons, photons and molecular vibrations.
Vibration levels of H₂.
Energy cannot be zero due to uncertainty.
In more detail
The quantum harmonic oscillator has equally spaced energy levels, E_n = (n + ½)ħω. It is the quantum version of SHM and underpins models of molecular vibrations and quantum fields.
Real-world uses
- Quantum field theory treats each mode of a field as a harmonic oscillator.
- Vibrational energy levels in molecules are modelled with this oscillator.
- Physicists use the quantum harmonic oscillator to model vibrations of atoms in a crystal and the energy of photons in a cavity.
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Frequently asked questions
Why is there a half in the energy?
Because even at the lowest level there is zero-point energy, so the oscillator is never at rest.
What is the spacing?
Constant, equal to ħω between adjacent levels.
Why is there a half in the ground state energy?
Even at zero temperature, a quantum oscillator has a minimum energy of half the quantum, which is called zero-point energy.
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