There´s a particle of spin 1/2 of which the spatial degrees of freedom are neglected

Be as descriptive as possible in the process of solving the problem

1.- There´s a particle of spin 1/2 of which the spatial degrees of freedom are neglected.

1. Determine the possible results of a measurement of (+ ) / (where index 1 corresponds to the x component and index 3 to z).
2. At time t = 0 a measurement of (+ ) / is made. Calculate the probability P ( = ħ/2) that a measurement of S2, carried out at time t =  (that is, immediately after the first measurement), gives the result + ħ /2.

2.- At the instant t = 0 the square angular momentum  is measured simultaneously and its third component  of a particle “u” is obtained respectively 2 and + ħ. At time t =  L1 is measured and + ħ is obtained.

Now if  is measured again. What is the probability P ( = ħ) of obtaining + ħ as a result?

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