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Quantum measurements of physical quantities are usually described as idealmeasurements. However, only a few measurements fulfil the conditions of idealmeasurements. The aim of the present work is to describe real positionmeasurements with detectors that are able to detect single particles. For thispurpose, a detector model has been developed that can describe the timedependence of interactions between nonrelativistic particles and a detector. Atthe beginning of a position measurement, the detector behaves as a targetconsisting of a large number of quantum mechanical systems. The incident objectinteracts with a single atom, electron or nucleus, but not with the wholedetector. This reaction is a quantum mechanical process. At the end of themeasurement, the detector can be considered as a classical apparatus. Adetector is neither a quantum mechanical system nor a classical apparatus. Thedetector model explains why one obtains a well-defined result for eachindividual measurement. It further explains that, in general, it is impossibleto predict the outcome of the next measurement. The main advantage is that itdescribes real rather than only ideal measurements.

On the quantum mechanical description of the interaction between particle and detector