If ψ is an eigenfunction of a given operator A ^ ^ , then a definite quantity (the eigenvalue a) will be observed if a measurement of the observable A is made on the state ψ. Conversely, if ψ is not an eigenfunction of A ^ ^ , then it has no eigenvalue for A ^ ^ , and the observable does not have a single definite value in that case. Instead, measurements of the observable A will yield each eigenvalue with a certain probability (related to the decomposition of ψ relative to the orthonormal eigenbasis of A ^ ^ ).