[60 pts] consider a two-level system. an operator a representing observable a, has two normalized eigenstates vand 0-1 with eigenvalues 1 and -1, respectively. operator b, representing observable b, has two normalized eigenstates (42 + v34-1)/2 and (1344 – 24-1)/2 with eigenvalues 1 and -1, respectively. (a) [20 pts] compute [a] (find the corresponding 2x2 matrix in the basis {431,4-1}). (b) (20 pts] assume that the system is in state (42 +-1)/v2. compute the variances o =< a> -< â> ? and off and check the uncertainty relation. (c) [20 pts] suppose that observable a was measured once at a certain time. right after the measurement, the expectation value of b for the system was 1/2. then, what would be the expectation value of a for this system?