2 '2 2. Two-dimensional harmonic oscillator: Consider a two-dimensional simple-harmonic oscillator H = MT\" + 2 2 , . WT?" = (dim + 1/2) + (dang + 1/2), Where a] = m%, and a2 = if. You are given an as yet unknown state |1,b) that lives in the Hilbert space of this system, and it is also given that the mean energy (nU|H|i,-9) = 2 While the variance of energy (t|H2|1,/)) (1/J|H|i,/))2 : 0. Our goal is to determine it) We assume that we can prepare the same state W) as many times as one likes so as to calculate any observable W'IOW)- (a) Suppose you are given that (which agagiw) = z, where z is some known constant. Argue that this is not enough to uniquely determine hp) (upto an overall phase factor). (b) Suppose, in addition to the information in part (a), you are also given that {laiag + (titular!) = a? where a: is again a known constant. Is this enough to determine the state WJ) (upto an overall phase factor). If yes, nd lib) If no, argue why it is not possible