The Hamiltonian of a two level system is given by - Â = E。[|1X(1| — |2X(2|] + E₁[11X(2| + |2X1|] where |1) and [2) is an orthonormal basis and Eo and E₁ are constants > 0 with units of energy. (a) Find the eigenvalues and corresponding eigenvectors of Â. Make sure the eigenvectors are propely normalized. (b) If at time t = 0, the system starts out in the state (6) Find the time evolution of the state of the system at later times, IS (t)). |S (0)) =
The Hamiltonian of a two level system is given by - Â = E。[|1X(1| — |2X(2|] + E₁[11X(2| + |2X1|] where |1) and [2) is an orthonormal basis and Eo and E₁ are constants > 0 with units of energy. (a) Find the eigenvalues and corresponding eigenvectors of Â. Make sure the eigenvectors are propely normalized. (b) If at time t = 0, the system starts out in the state (6) Find the time evolution of the state of the system at later times, IS (t)). |S (0)) =
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![The Hamiltonian of a two level system is given by
 = Eo[11X(1| − |2)(2|] + E₁[11X2| + |2X(1|]
where [1] and [2) is an orthonormal basis and Eo and E₁ are constants > 0 with units of energy.
(a) Find the eigenvalues and corresponding eigenvectors of Â. Make sure the eigenvectors
are propely normalized.
(b) If at time t = 0, the system starts out in the state
|S (0))
(6)
Find the time evolution of the state of the system at later times, IS (t)).
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18ff836d-3cc8-4a2b-b721-7f7a69fbe250%2F27a99a2f-8645-4b79-8eb0-7ccb40488c68%2Fh6kvj87_processed.png&w=3840&q=75)
Transcribed Image Text:The Hamiltonian of a two level system is given by
 = Eo[11X(1| − |2)(2|] + E₁[11X2| + |2X(1|]
where [1] and [2) is an orthonormal basis and Eo and E₁ are constants > 0 with units of energy.
(a) Find the eigenvalues and corresponding eigenvectors of Â. Make sure the eigenvectors
are propely normalized.
(b) If at time t = 0, the system starts out in the state
|S (0))
(6)
Find the time evolution of the state of the system at later times, IS (t)).
=
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