  Quantum measurements of physical quantities are usually described as ideal
measurements. However, only a few measurements fulfil the conditions of ideal
measurements. The aim of the present work is to describe real position
measurements with detectors that are able to detect single particles. For this
purpose, a detector model has been developed that can describe the time
dependence of interactions between nonrelativistic particles and a detector. At
the beginning of a position measurement, the detector behaves as a target
consisting of a large number of quantum mechanical systems. The incident object
interacts with a single atom, electron or nucleus, but not with the whole
detector. This reaction is a quantum mechanical process. At the end of the
measurement, the detector can be considered as a classical apparatus. A
detector is neither a quantum mechanical system nor a classical apparatus. The
detector model explains why one obtains a well-defined result for each
individual measurement. It further explains that, in general, it is impossible
to predict the outcome of the next measurement. The main advantage is that it
describes real rather than only ideal measurements.
