The simple harmonic and anharmonic oscillator are two important systems met in quantum mechanics.
The potential energy of a particle that can be mapped by simple harmonic oscillation is shown above.
- The energy splitting is either ħω which is equivalent to hv0.
- The energy splittings are equal to one another.
- The lines on either side are not asymptotic on the y axis; this means the particles can technically pass through each other.
Anharmonic/ Quantum harmonic oscillator.
- The energy spacing is not equal between the energy levels.
- The potential energy barrier does not cross the y axis as the nuclei cannot pass through one another.
- The molecule dissociates at the largest separation.
- Comparison shows that the quantum harmonic oscillator is pulled up on the left hand side.
- The right hand side has a tailing off of energy.