On the feasibility and usefulness of applying the `Schr\"odinger c.q. Liouville-von Neumann equation' to quantum measurement

Abstract

The present paper is a sequel to papers dealing with recent developments on the issue of `quantum measurement'. In this paper `measurement within the domain of application of quantum mechanics' is treated as a \emph{quantum mechanical} \emph{interaction} of a `(sub)microscopic object $(o)$' and an `equally (sub)microscopic part of the measuring instrument $(a)$ being sensitive to the (sub)microscopic information', that interaction to be described by a Schr\"odinger equation. The Stern-Gerlach experiment is used as a paradigmatic example. An alternative to the Heisenberg inequality is found, exhibiting the \emph{independent} contributions of `preparation of the initial state of object $(o)$' \emph{and} `interaction of object $(o)$ \emph{and} measuring instrument/probe $(a)$'. Applicability of the Liouville-von Neumann equation is stressed.