Let VA), VB) be the eigenvectors of the Hamiltonian Ĥ of a two-level systemĤVA,B) = EA,BVA,B) EA> EB.Another basis ₁), 2), withis related to A), VB) by(W₁|yj) = Sij i, j = 1,2|WA,6) = √2(191₁) ±|y₂)).Find the matrix elements of the Hamiltonian Â' in the basis ₁), 2) using thedyadic notation and the matrix notation. Then, assuming that at time t=0 the systemis in ₁), find the time evolved state using the time dependence of the Ĥ eigenstates,and calculate the time t such that for the first time the system has probability 1 tobe in 2). Show how one obtains the same result by the time evolution operator.Assume ħ 1 for simplicity.

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Answered: Let VA), B) be the eigenvectors of the…

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