A number of spin 1/2 particles are run through a Stern-Gerlach apparatus and when the emerge they all have the same spin wave function (ψ1, ψ2)τ and 9/25 are in the +z direction and 16/25 are in the -z direction with the normal basis column vectors for +z and -z.
Determine a possible normalized spin wave function
The Attempt at a Solution
I am not sure where to start, all i can think of is to have 9/25(+z) = (9/25,0)τ and 16/25(-z) = (0, 16/25)τ to yield a total wave function of (9/25,16/25)τ
but I don't know what to do for the normalization or if my initial thought was even on the right track? Thanks for the guidance!