PHY4221: Homework 9 Due Nov. 13, 2008 1. For the angular momentum state | ψ i = | j,m j = j i , calculate the variance of each com-ponent of the angular momentum operator. 2. Calculate the mean and variance of the J x for the state | ψ i = e-iπJ y / (2 ~ ) | j,m j = j i . 3. A spin-1 particle has the Hamiltonian, H = αJ 2 + β ( J 2 + + J 2-) where α and β are constants. (a) Find the matrix form of the H in the basis of | j,m j i . (b) Find the eigenvalues and eigenvectors of H . (c) Determine the time-dependent state vector if the initial state is given by | j = 1 ,m j = 1 i . Use your result to ﬁnd the expectation value
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