The Hamiltonian of a two level system is given by Ĥ = Eo[1)(2| + Eol2)(1| where |1) and |2) is an orthonormal basis and Eo is a constant > 0 with units of energy. (a) Find the eigenvalues and corresponding eigenvectors of Ĥ. Make sure the eigenvectors are propely normalized. (b) If at time t = 0, the system starts out in the state || |S(0)) = ) Find the time evolution of the state of the system at later times, |S(t)).
The Hamiltonian of a two level system is given by Ĥ = Eo[1)(2| + Eol2)(1| where |1) and |2) is an orthonormal basis and Eo is a constant > 0 with units of energy. (a) Find the eigenvalues and corresponding eigenvectors of Ĥ. Make sure the eigenvectors are propely normalized. (b) If at time t = 0, the system starts out in the state || |S(0)) = ) Find the time evolution of the state of the system at later times, |S(t)).
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Transcribed Image Text:Operators: Spectral Representation
The Hamiltonian of a two level system is given by
Ĥ = Eo[1)(2| + Eol2)(1|
where |1) and |2) is an orthonormal basis and Eo is a constant > 0
with units of energy.
(a) Find the eigenvalues and corresponding eigenvectors of H.
Make sure the eigenvectors are propely normalized.
(b) If at time t
0, the system starts out in the state
()
|S(0) =
Find the time evolution of the state of the system at later
times, IS(t)).
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