The superposition principle is closely related to the notion of incompatible observables:
an eigenstate of an observable Ô1 can be written as a superposition of eigenstates of another observable Ô2 if and only if Ô1 and Ô2 are incompatible observables i.e. their commutator is nonzero.
The actual system state is an eigenstate belonging to an observable and is therefore an expansion (i.e. superposition) of eigenfunctions of the corresponding incompatible observable.
Subconsequently, the superposition principle is also related to quantum indeterminacy.
In conclusion, the superposition principle, incompatible observables and quantum indeterminacy are closely related notions.
Remember:
- observables are (represented by) hermitian operators. The eigenvectors represent possible system states and the corresponding real eigenvalues are the possible outcomes.
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