To the quantum mechanics specialists community it is a well-known fact that the famous original Stern–Gerlach experiment (SGE) produces entanglement between the external degrees of freedom (position) and the internal degree of freedom (spin) of silver atoms. Despite this fact, almost all textbooks on quantum mechanics explain this experiment using a semiclassical approach, where the external degrees of freedom are considered classical variables, the internal degree is treated as a quantum variable, and Newton's second law is used to describe the dynamics. In the literature there are some works that analyze this experiment in its full quantum mechanical form. However, astonishingly, to the best of our knowledge the original experiment, where the initial states of the spin degree of freedom are randomly oriented coming from the oven, has not been analyzed yet in the available textbooks using the Schrödinger equation (to the best of our knowledge there is only one paper that treats this case: Hsu et al (2011 Phys. Rev. A 83 012109)). Therefore, in this contribution we use the time-evolution operator to give a full quantum mechanics analysis of the SGE when the initial state of the internal degree of freedom is completely random, i.e. when it is a statistical mixture. Additionally, as the SGE and the development of quantum mechanics are heavily intermingled, we analyze some features and drawbacks in the current teaching of quantum mechanics. We focus on textbooks that use the SGE as a starting point, based on the fact that most physicist do not use results from physics education research, and comment on traditional pedagogical attitudes in the physics community.

A full quantum analysis of the Stern-Gerlach experiment using the evolution operator method: analysing current issues in teaching quantum mechanics E Benítez Rodríguez, L M Arévalo Aguilar and E Piceno Martínez -Applying classical geometry intuition to quantum spin

Abstract:The Stern-Gerlach experiment (SGE) is one of the foundational experiments in quantum physics. It has been used in both the teaching and the development of quantum mechanics. However, for various reasons, some of its quantum features and implications are not fully addressed or comprehended in the current literature. Hence, the main aim of this paper is to demonstrate that the SGE possesses a quantum nonlocal character that has not previously been visualized or presented before. Accordingly, to show the nonlocality into the SGE, we calculate the quantum correlations C(z, θ) by redefining the Banaszek-Wódkiewicz correlation in terms of the Wigner operator, that is C(z, θ) = Ψ|Ŵ(z, p z )σ(θ)|Ψ , whereŴ(z, p z ) is the Wigner operator,σ(θ) is the Pauli spin operator in an arbitrary direction θ and |Ψ is the quantum state given by an entangled state of the external degree of freedom and the eigenstates of the spin. We show that this correlation function for the SGE violates the Clauser-Horne-Shimony-Holt Bell inequality. Thus, this feature of the SGE might be interesting for both the teaching of quantum mechanics and to investigate the phenomenon of quantum nonlocality.