S. Albeverio et al., REPRESENTATION OF THE SOLUTIONS OF THE BE LAVKIN QUANTUM MEASUREMENT EQUATION BY A RIGOROUS VERSION OF THE MENSKI FUNCTIONAL-INTEGRATION FORMULA, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 323(6), 1996, pp. 661-664
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.