Depends on the experiment.<p>If it is a &quot;perfect experiment&quot; (gedankenexperiment), and you measure the spin in the same direction a second time while not perturbing the experiment in anyway, the state should be in the state you measured it before. It is now an eigenstate of the spin operator (say, if you measured in a direction z, it is an eigenstate of S_z) and it will stay that way until it is disturbed.