SIMPLE REALIZATIONS OF GENERALIZED MEASUREMENTS IN QUANTUM-MECHANICS

This paper discusses the approach to the analysis of measurements in quantum mechanics which is based on a set of ''detection operators'' forming a resolution of identity. The expectation value of each of these operators furnishes the counting rate at a detector for any object state that is prepared. ''Predictable measurements'' are those for which there is a representation in which only one element of each diagonal matrix representing each operator is not zero. A set of commuting detection operators defines the class of ''spectral measurements'', which may be either predictable or not. An even more general definition of measurement may be given by abandoning the requirement of commutativity of the detection operators. In this case one cannot define an observable which corresponds to a single self-adjoint operator, which violates the standard theory of quantum mechanical measurement. Simple experimental realizations of each of these classes of measurement are suggested.