The Hamiltonian of a certain system is given by [1 0 0 H = hw |0 0 0 Lo 0 1 Two other observables A and B are represented by i 0 A = a|-i 0 0 0 0 1 [1 0 0 B = b0 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 lµ(0) >= 2c -c where c is a real constant. Determine the normalized state |p(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
The Hamiltonian of a certain system is given by [1 0 0 H = hw |0 0 0 Lo 0 1 Two other observables A and B are represented by i 0 A = a|-i 0 0 0 0 1 [1 0 0 B = b0 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 lµ(0) >= 2c -c where c is a real constant. Determine the normalized state |p(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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![The Hamiltonian of a certain system is given by
[1 0
H = ħw]0
LO 0
1
Two other observables A and B are represented by
1 0 0
, B = b]0 2 0
lo o
0-
i 0
A = a|-i 0 0
0 1
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
lµ(0) >=
-c
2c
where c is a real constant. Determine the normalized state |(t) >.
c. What are the eigenvectors of B?
d. Find the expectation values of A and B in the state |p(t) >, and hence determine if A and B are
conservative observables](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7a4f0460-4d37-4752-b532-6f2b1704fac3%2F1eb436d4-fb9d-48a7-b6f9-90d2759d0285%2F5yi6dmq_processed.png&w=3840&q=75)
Transcribed Image Text:The Hamiltonian of a certain system is given by
[1 0
H = ħw]0
LO 0
1
Two other observables A and B are represented by
1 0 0
, B = b]0 2 0
lo o
0-
i 0
A = a|-i 0 0
0 1
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
lµ(0) >=
-c
2c
where c is a real constant. Determine the normalized state |(t) >.
c. What are the eigenvectors of B?
d. Find the expectation values of A and B in the state |p(t) >, and hence determine if A and B are
conservative observables
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