A Hamiltonian for a certain two-level system is Ĥ = E(|1)(1| – |2)(2|+|1{2|+ |2){1|) where the kets |1) and |2) are the spin-up and spin-down eigenvectors of Sz, respectively. E is a constant with the units of energy. a) Find the matrix representation of the Hamiltonian in the basis |1) and |2). b) Find the energy levels of this two-level system c) Find the energy eigenstates of this two-level system
A Hamiltonian for a certain two-level system is Ĥ = E(|1)(1| – |2)(2|+|1{2|+ |2){1|) where the kets |1) and |2) are the spin-up and spin-down eigenvectors of Sz, respectively. E is a constant with the units of energy. a) Find the matrix representation of the Hamiltonian in the basis |1) and |2). b) Find the energy levels of this two-level system c) Find the energy eigenstates of this two-level system
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Hamiltonian two-level system
Transcribed Image Text:A Hamiltonian for a certain two-level system is
Ĥ = E(|1)(1| – |2)(2| +|1)(2| + |2)X1)
where the kets |1) and |2) are the spin-up and spin-down eigenvectors of S2, respectively. E is a constant with
the units of energy.
a) Find the matrix representation of the Hamiltonian in the basis |1) and |2).
b) Find the energy levels of this two-level system
c) Find the energy eigenstates of this two-level system
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