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Because it has disclosed basic quantum properties and concepts, the Stern-Gerlach experiment (SGE) has been fundamental for the development of quantum mechanics; for example, it was particularly used to model the measurement problem on the quantum world. Despite being almost one hundred years old, the SGE is still providing new valuable insights in the development and understanding of quantum mechanics. In this paper, by using the evolution operator method, we derive the equations that provide the time evolution of the quantum state of a particle with arbitrary spin s in the Stern-Gerlach apparatus. Such temporal evolution shows quantum entanglement between the degrees of freedom of the particle. We theoretically study, through the von Neumann entropy, the entanglement that arose between the degrees of freedom of the system for the case when the particle is polarized with an arbitrary angle $ \theta$ , analyzing how the entanglement depends on this angle $ \theta$ . |
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