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I was told that if you put a spin 1/2 particle in a magnetic field, it will align with or against the field. But some places it also says that it will precess around the field. Which one is right?
Spin up and spin down are not defined using magnetic moments. They usually mean the z-component of the spin vector (expectation) is +hbar/2 or -hbar/2 for up or down respectively.