REPRESENTATION OF THE SOLUTIONS OF THE BE LAVKIN QUANTUM MEASUREMENT EQUATION BY A RIGOROUS VERSION OF THE MENSKI FUNCTIONAL-INTEGRATION FORMULA

In 1979, Menski suggested a formula for the propagator of a quantum sy stem with continuously observed position in terms of the heuristic Fey nman path integral. In 1988, the a posteriori Schrodinger equation was written (in general form by Belavkin and for an important particular case by Diosi) describing the evolution of a quantum system under cont inuous (nondemolition) measurement. In the present paper, two mathemat ically well defined representations of the solution of the a posterior i Schrodinger equation (corresponding to the continuous observation of the position of a quantum particle) in terms of a mathematically well defined path integral (valid for different conditions on initial func tion and potential) am provided It turns out that the so formulas obta ined are formally equivalent with the one suggested by Menski.