Quantum-Mechanical Measurement Operator

A unitary operator is defined, connecting the states of the measured system and the measuring-instrument system before and after interaction, by means of which the post-interaction values of $S$ in the instrument can be used to calculate the pre-interaction ${〈R〉}_{\mathrm{av}}$ and ${\Delta }^{2}R$ in the measured system, where $R$ and $S$ are Hermitian operators. The premeasurement state of the instrument need not be known, and the same measurement operator is applicable whether the system to be measured is originally described by a pure case or a mixture. Finally, this theory is contrasted briefly with the measurement theory of von Neumann.