Discuss the below:
Eigenvalues, eigenvectors, and time evolution
Q1 Given matrix A = 1 2 0 where i found the eigenvalues to be 3hw, 0, -3hw.
2 0 2
0 2 -2
then if at t=0 state-vector is 1 THEN compute the state vector at time t.
0
0
Q2. If A = 1 0 0 is an observable. FIND its expectation at time t and compute the
0 2 0
0 0 0
probability that measuring A at time t gives the result 1.