It is known that there is a 36 probability of obtaining Sz

It is known that there is a 36% probability of obtaining Sz = h/2 and therefore a 64% chance of obtaining Sz = h/2 if a measurement of Sz is carried out on a spin-1/2 particle. In addition, it is known that the probability of finding the particle with Sx = h/2, that is in the state |+x), is 50%. Determine the state of the particle as completely as possible from this information.

Solution

S_z with eigen value h/4pie---------36% probaility

S_z with eigen value ^-h/4pie---------64% probaility

S_x with eigen value h/4pie---------50% probaility

S_xwith eigen value ^-h/4pie---------50% probaility

S_y has also equal probabaility as that of S_x

S_y with eigen value h/4pie---------50% probaility

S_ywith eigen value ^-h/4pie---------50% probaility