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The Hamiltonian of a certain system is given by
0 0
H = ħw|0 _0 0
0 1
1
Two other observables A and B are represented by
A = a|-i 0 0
0 0 1
[1 0 0
B = b|0 _2 0
Lo o 2
w, a, b are positive constant.
a. Find the eigenvalues and normalized eigenvectors of H
b. Suppose the system is initially in the state
2c
ly(0) >=
2c
where c is a real constant. Determine the normalized state |4(t) >.
c. What are the eigenvectors of B?
d. Find the expectation values of A and B in the state [Þ(t) >, and hence determine if A and B are
conservative observables

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