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Why is it not possible to do the stern gerlach experiment in a uniform field? What makes it non classical?

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Because in uniform fields there is no net force on the atoms, regardless of their magnetic dipole moment. The energy of the interaction has the form $$ U = - \vec \mu\cdot\vec B(\vec r) = -g\,\vec\sigma\cdot\vec B(\vec r); $$ the force is given by the spatial gradient of the energy (and the torque by its gradient with respect to orientation). Thus, in a uniform field, there is no gradient, no force, and no way to spatially separate the atoms by their magnetic dipole - which is what Stern-Gerlach magnets are meant to be doing.

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Because there would not be a net force on the atom and so it would not be deflected.
The forces could act as a couple which would produce a rotational motion but no translation motion.

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The Stern-Gerlach experiment in its entirety can be seen as a semiclassical: the translational degrees of freedom can be well-approximated by classical motion whereas the internal degree of freedom is quantum. You need a magnetic field gradient to obtain a net deflection of the two spin components as they pass through the magnet for otherwise the potential $U$ Emilio defined above would be constant.

You can find an in-depth explanation of this in Section 5 of Gat, Lein & Teufel, Annales Henri Poincaré 15, 1967 (2014).

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