The time dependence of quantum-state amplitudes is calculated and experimentally demonstrated for the spin states of the rubidium atom. The mechanism of optical pumping is used to prepare the spin state oriented along the z axis. The magnetic field is then quickly switched from the z to the x direction and the light transmitted through the rubidium vapor is used as a probe to measure the probability that the atoms are in the various quantum states with respect to the z axis. The time dependence of absorbed light is calculated, first for the simplified case of spin 12, then for spin 1, and finally for spin 2, which is the value observed in the experiment.

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