6. Consider a molecule interacting with a bath. Let a and b be two nondegenerate eigenstates of the isolated-molecule Hamiltonian H having energy eigenvalues a and b, respectively. Consider three different possibilities for the density operator of this system at time t =0 1(0)=where=21(a+b)2(0)=where=21(ab)3(0)=21(aa+bb) The first two correspond to pure cases while the third is a statistical mixture. (a) Give the 22 matrix representation of the density operator in the {a,b} basis for each of the three situations. (b) Calculate the population of state a for each of the three situations. (c) Assume the matrix elements of the dipole moment operator in the {a,b} basis are a^a=b^b=0, that is there is no permanent dipole moment in either eigenstate, and a^b=b^a=, a real vector quantity representing the transition dipole moment connecting the eigenstates. Calculate the expectation value of the dipole moment, ^, for each of the three situations