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The Stern-Gerlach experiment shows that spin particles through an inhomogeneous magnetic field are scattered as if their magnetic moment in the direction of the magnetic field could only be $\pm \frac{1}{2}$. It also tells that once a particle has "chosen" the positive or negative value, if the particle goes through another Stern-Gerlach apparatus it will keep its former value.

According to this, I would expect the particle spinor to be aligned with the field, however, according to the Schrödinger equation, it seems that the only change that the magnetic field does on the spinor is a Larmor precession over the plane that is perpendicular to the magnetic field, without aligning the spinor with the magnetic field.

Do you know if the spinor gets aligned with the magnetic field in quantum theory using the Schrödinger equation, or perhaps using the Dirac equation?

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"In quantum mechanics, the Pauli equation or Schrödinger–Pauli equation is the formulation of the Schrödinger equation for spin-½ particles, which takes into account the interaction of the particle's spin with an external electromagnetic field. It is the non-relativistic limit of the Dirac equation and can be used where particles are moving at speeds much less than the speed of light, so that relativistic effects can be neglected. It was formulated by Wolfgang Pauli in 1927" .

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