Do commuting operators share the same eigenfunctions?

[Brewer]

Just a quickie:

If two operators commute, what can be said about their eigenfunctions?

The only thing I can glem from the chapter in my textbook about this is that the eigenfunctions are equal? Is this right, or have I misread it?

 

[cristo]

If two (Hermitian) operators commute, then there exists a complete set of eigenvectors which is common to both operators.

 

[Sojourner01]

Not to interrupt, but if I were asking this question, I'd be doing so exclusively in terms of wave mechanics. It seems to be the 'mdern' way to ignore matrix mechanics when teaching QM - at least it is for my department.