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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 00 0 1 [1 0 0 B = b|0 2 0 Lo 0 2 w, a, b are positive constant. a. Find the eigenvalues and normalized eigenvectors of H

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 00 0 1 [1 0 0 B = b|0 2 0 Lo 0 2 w, a, b are positive constant. a. Find the eigenvalues and normalized eigenvectors of H

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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
Transcribed Image Text: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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