I have this take home I would like some help on thanks: "The spin components of a beam of atoms prepared in the state |ψ>are measured and the following experimental probabilities are obtained: P+z=1/2 P-Z=1/2 P+x=3/4 P-x=1/4 (i.e., if the beam of atoms goes through a single Stern-Gerlach setup in the x-direction, 3/4 of the particles are measured to have spin up in the x-direction and 1/4 of the particles are measured to have spin down in the x-direction.) 1. From the experimental data, determine the input state as a linear combination of |=>z and |->z (i.e. determine as much of each coefficient of the two states in the sum). Show your work. With no lossof generality, you may assume that the coefficient of |+>z is real but the coefficient of |->z is not. 2. Determine P+y and P-y." here's my attempt: the linear combination I got is 1/(2)^1/2 for |+>z and -i/(2)^1/2 for |->z. Not sure where to go from there. Thanks for any help I can get!