We present, in various limits, analytical expressions for the center-of-mass wave function of a spin-1/2 atom as it is deflected by a Stern-Gerlach apparatus.

The many-Hilbert-spaces theory of quantum measurements, which was originally proposed by S. Machida and the present author, is reviewed and developed. Dividing a typical quantum measurement in two successive steps, the first being responsible for spectral decomposition and the second for detection, we point out that the wave packet reduction by measurement takes place at the latter step, through interaction of an object system with one of the local systems of detectors. First we discuss the physics of the detection process, (...) using numerical simulations for a simple detector model, and then formulate a general theory of quantum measurements to give the wave packet reduction in an explicit form as a sort of phase transition. The derivation is based on the macroscopic nature of the local system, to be represented in a continuous direct sum of many Hilbert spaces, and on the finite-size effect of the local system, to give phase shifts proportional to size parameters. We give a definite criterion for examining any instrument as to whether it works well as a detector or not. Finally, we compare the present theory with famous measurement theories and propose a possible experimental test to discriminate it from others. A few solvable detector models are also discussed. (shrink)

The possibilities of a realistic interpretation of quantum mechanics are investigated by means of a statistical analysis of experiments performed on the simplest type of quantum systems carrying spin or helicity. To this end, fundamental experiments, some new, for measuring polarization are reviewed and (re)analyzed. Theunsharp reality of spin is essential in the interpretation of some of these experiments and represents a natural motivation for recent generalizations of quantum mechanics to a theory incorporating effect-valued measures as unsharp observables and generalized (...) systems of imprimitivity. (shrink)