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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) = a

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?

Answers

be then page- of last The eigen reeks of 193) observable A, Alay a lay Ala) alan) Henniltonian of the system; d - 2. The H 2Vector at time to the t 15 Page 3 sinnilarly of of the eigen 1 az? State vecks of the system at time 1927 et il - (4) ei The

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