Models of particle detection in regions of space-time

We investigate two models of measuring devices designed to detect a nonrelativistic free particle in a given region of space-time. These models predict different probabilities for a free quantum particle to enter a space-time region R; therefore, this notion is device dependent. The first model is of a von Neumann coupling, which we present as a contrast to the second model. The second model is shown to be related to probabilites defined through partitions of configuration-space paths in a path integral. This study thus provides insight into the physical situations to which such definitions of probabilities are appropriate.