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Consider a quantum system with three states and a Hamiltonian given by 1 2ε 0 Ĥ = H₂ 2ε 1 3ε 0 3ε 4 where Ho is a constant and the perturbation parameter is small (ɛ << 1). a. 0). Write down the eigenvalues and eigenvectors of the unperturbed Hamiltonian (e =

Consider a quantum system with three states and a Hamiltonian given by 1 2ε 0 Ĥ = H₂ 2ε 1 3ε 0 3ε 4 where Ho is a constant and the perturbation parameter is small (ɛ << 1). a. 0). Write down the eigenvalues and eigenvectors of the unperturbed Hamiltonian (e =

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Consider a quantum system with three states and a Hamiltonian given by 1 Ho 28 1 2ε 0 3ɛ 3ɛ 4 0 where Ho is a constant and the perturbation parameter is small (ɛ « 1). a. b. C. 0). Ĥ = Write down the eigenvalues and eigenvectors of the unperturbed Hamiltonian ( = Find the leading correction energy to the state that is nondegenerate in the zeroth- order Hamiltonian. Use degenerate perturbation theory to find the first-order corrections to the two initially degenerate energies.
Transcribed Image Text:Consider a quantum system with three states and a Hamiltonian given by 1 Ho 28 1 2ε 0 3ɛ 3ɛ 4 0 where Ho is a constant and the perturbation parameter is small (ɛ « 1). a. b. C. 0). Ĥ = Write down the eigenvalues and eigenvectors of the unperturbed Hamiltonian ( = Find the leading correction energy to the state that is nondegenerate in the zeroth- order Hamiltonian. Use degenerate perturbation theory to find the first-order corrections to the two initially degenerate energies.
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