Quantum-mechanical models of position measurements

A systematic construction of exactly solvable models of interactions between the measuring apparatus and the particle whose position is to be measured is shown. The two types of root-mean-square errors are calculated for these models and many new models with better statistics than the standard von Neumann model are continuously found. The best among them is the model which has been shown to circumvent the standard quantum limit for the position monitoring. A feature of the models similar to Bondurant's improvement of the interferometric position measurement is also pointed out.