Quantum measurement noise for observation of a particle in a magnetic field

The quantum theory of continuous measurements based on Feynman integration “in finite limits” is used in the problem of following the coordinates of a particle moving in a magnetic field. The probability of a particular result of the following for known external force is found, and, conversely, the accuracy with which the external force can be recovered from the known result of measurement is estimated. Allowance is made not only for the spread of the results due to instrumental error but also for the quantum-mechanical influence of the measuring process on the motion of the particle. Three characteristic regimes of measurement are identified: classical, quantum, optimal.