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European Journal of Physics

Quantum mechanical description of the Stern-Gerlach experiment

S. H. Patil

Published Jan 1, 1998• 13 citations
Publisher

Abstract

It is emphasized that the Stern-Gerlach experiment may be described in terms of the time evolution of the state vector in the presence of a linear potential and a spatial collapse at the screen.
DOI
10.1088/0143-0807/19/1/005

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The Stem-Gerlach (SG) experiments considered as a quantum measurement process measuring the spin states of particles from their spatial distribution. The wave packet collapse or quantum decoherence can he described as a dynamical evolution governed by the interaction between the space degrees of freedom and the spin degrees of freedom. The analytic solution of this exactly solvable model shows that the decaying process of coherence with time in the SG experiment obeys no longer the linear exponential law.
Most textbooks introduce the concept of spin by presenting the Stern-Gerlach experiment with the aid of Newtonian atomic trajectories. However, to understand how both spatial and spin degrees of freedom evolve over time and how the latter influence experimental outcomes, it is essential to employ a quantum approach. In this paper, we offer two simple methods, the Baker-Campbell-Hausdorff formula and the direct integration of the Schrödinger equation in an interaction picture, to determine the corresponding evolution operator. We not only provide an interpretation of the individual terms within this operator but also establish connections with semiclassical calculations, when feasible. Moreover, we compute the wave function and touch upon the concept of position-spin entanglement to illustrate how a full quantum description of the Stern-Gerlach experiment can open doors to topics like quantum measurement and nonlocality.