B.S.T.J. Brief: On the Simultaneous Measurement of a Pair of Conjugate Observables

T H E BELL SYSTEM TECHNICAL J O U R N A L , A P R I L 1965 which we will call the "balance," having to do with how near our joint measurement is to either of two ideal measurements. To effect the desired measurement, the coupling must be described by the following Hamiltonian: Hint = K(qPx + pPv) (1) where p,q are the positions and momentum we wish to be measured and P x , P y are the momenta of the two single-degree-of-freedom systems we are using for meters. The positions of the two meters will be x and y. In addition, we require t h a t the meters initially be in the states M(.r) and N(y), where n o (2) N(y) = - ) e -62/2 and b is the "balance." The strength of the interaction K is assumed to be sufficiently large t h a t other terms in the Hamiltonian can be ignored. Hence the Schrodinger equation will be (fi = 1) dip dt V dx dqdyj with the initial condition