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The term "harmonic oscillator" is used to describe any system with a "linear" restoring force that tends to return the system to an equilibrium state. There is both a classical harmonic oscillator and a quantum harmonic oscillator. Both are used as toy problems that describe many physical systems.

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Hilbert space of a diatomic molecule

In molecular quantum mechanics, it is very common to model a diatomic molecule as a two-level harmonic oscillator with vibrational levels lying within the electronic states: In most of the textbooks …
Cedric Chia's user avatar
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Overlap integral between harmonic oscillators of different shapes

In a diatomic molecule, the nuclear potential in the ground and excited states can take different shapes. The coordinates might be displaced and the curvatures might not be the same. For example, we m …
Cedric Chia's user avatar