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The Stern-Gerlach Experiment

Send a beam of atoms through a magnet whose field is stronger on one side than the other and the field grabs each atom by its magnetic moment, tugging it sideways by an amount set by how the moment is tilted. A classical spinning charge could point any way at all, so the beam should fan out into a continuous smear, a vertical streak on the far screen. In 1922 Stern and Gerlach saw something else: the beam split cleanly into two, two sharp spots with a gap between them and nothing in the middle. The tilt of the moment is quantised. A spin-1/2 atom has only two allowed orientations, $m_s = \pm\tfrac{1}{2}$, so only two deflections, and in general a spin-$s$ beam fractures into exactly $2s+1$ spots, which is how the experiment weighs the spin: count the spots. The top panel fires atoms one at a time, each picking a random allowed state and deflecting by it, and watches the discrete spots build up dot by dot inside the faint band where the classical smear would have landed. The bottom panel is the screen read as an intensity profile, the quantum delta-like peaks standing where a flat classical density would have spread. Dial the field gradient to spread the spots, and switch the spin to watch the spot count change.

Figure 1. The Stern-Gerlach experiment. Top: atoms from the oven pass the inhomogeneous magnet (N wedge, S flat) and deflect by their quantised m_s into 2s+1 spots on the screen, inside the faint blue band a classical moment would smear across. Bottom: the screen intensity profile, sharp quantum peaks against the flat classical band. Method: discrete m_s sampling, deflection proportional to m_s. Source: Griffiths, Introduction to Quantum Mechanics, 2nd ed., Sec. 4.4.1.
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WHAT TO TRY

  • Watch the spots build dot by dot: discrete clusters form with empty gaps, never the continuous streak the classical picture predicts.
  • Switch the spin: a spin-1/2 beam gives two spots, spin-1 gives three, spin-3/2 gives four, the count is $2s+1$.
  • Raise the field gradient to push the spots farther apart; the deflection is proportional to it.
  • Compare with the faint classical band: the quantum spots sit inside where the continuous smear would have landed.