I know that using Mathematica you can obtain the eigenvalues and eigenvectors of a matrix. I was wondering if using Mathematica you can obtain the common eigenvalues and eigenvectors of a couple of matrices which commute. This is a typical problem in Quantum Mechanics: when you have two observables represented by matrices, A and B, if they both commute, i.e. if AB=BA, then you can find a common basis associated to them.

Is there any option in Mathematica that can do this?

Thanks in advance!!!

Rafa.