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# Consider a two-dimensional state vector space and a basis in this space lay), laz), eigenvectors of...

###### Question:

Consider a two-dimensional state vector space and a basis in this space lay), laz), eigenvectors of an observable A: Ala) = aja) Alaz) = azlaz) A representation of Hamiltonian operator in this basis is: H = (8 5) Find: -Eigenstates and eigenvalues of H. -If the system is in state |az) at time t=0, What is the state vector of the system at time t? -What is the probability of finding the system in the state |az) at time t? -Calculate the dispersion of measurements of A and Hat time t. Is the uncertainty principle Energy x Time fulfilled?

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