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Quantum harmonic oscillator
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Equally spaced levels with zero point energy.
E_n = (n+½)ħωEnergy levels E_n = (n + ½)ħω are equally spaced; the wavefunctions are Hermite polynomials times a Gaussian. It models vibrations of molecules, phonons and fields.
Photons are quanta of an EM oscillator.
Spacing is ħω.
In more detail
The quantum harmonic oscillator has energy levels E_n = (n + ½)ħω, equally spaced, with a zero-point energy. It is the quantum version of a vibrating spring or bond.
Real-world uses
- Molecular vibrations are modelled as harmonic oscillators.
- Quantum field theory uses oscillators for each mode of a field.
- Chemists model molecular vibrations as harmonic oscillators, which predicts the infrared spectra of molecules.
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Frequently asked questions
What is zero-point energy?
The lowest energy, ½ħω, which is never zero for a quantum oscillator.
Are the levels equally spaced?
Yes, for the ideal harmonic oscillator.
Why are the energy levels evenly spaced?
For a quantum oscillator, the levels are separated by the same amount, Planck's constant times the frequency.
Related topics in Quantum Mechanics
Quantum tunnelling · Tunnelling applications · Alpha decay as tunnelling · Zero point energy · Hydrogen atom in quantum mechanics · Quantum numbers