  The quantum mechanical expression relating two commuting operators is
reformulated such that the power method (also called method of moments) for
iteratively calculating eigenvalues and eigenvectors becomes applicable. The
new iterative scheme thus obtained allows to pre-select a quantum number of one
of the two commuting operators and then calculate a corresponding eigenvalue of
the other operator. The result is the common eigenvector of the eigenvalue
pair. Among others the method may be used to calculate excited states, cope
with degeneracy and/or accelerate convergence. Small example calculations are
presented as a 'Proof-of-Concept' and to reveal some properties of the new
method.
