# Why are wave functions orthogonal?

It seems that all wave functions studied in physical chemistry are orthogonal (e.g. particle in a box, hydrogen atomic orbitals). Does this come about because we purposefully make them orthogonal, or are they derived that way naturally? Can there be useful wave functions that are not orthogonal?

• They are eigenfunctions of a hermitian operator. – user26143 Nov 22 '13 at 9:10

• Eigenvectors are not orthogonal "by definition". It's just that two eigenvectors of a Hermitian operator $A$, to different eigenvalues, are necessarily orthogonal (else e.g. decomposing in the middle of $A^2$ would lead to contradiction). They're however typically normalised by definition, thus orthonormal. – leftaroundabout Apr 29 '14 at 20:16