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3 Hydrogen and the Postulates [32 points] energies as multiples of the Bohr energy Eo. All basis states are labeled by {|n, e, m) } as usual. For this problem we will consider an electron in a hydrogen potential. In this problem express We all will ignore the electron's spin in this problem! Postulate 2 (Observables): The electric dipole moment vector is an observable whose op- erator is given by d = -ef. Consider the equal 1s-2p superposition state given at time t = 0 by 1 + (a) [6 points] Show that the expectation value of the dipole moment vector is oscillatory in time for the state ((t)). That is, show (d2) = Acoswt. You will have to determine the frequency and amplitude of oscillation w and A. [Note: There are a few groundwork steps you will have to do! One first step would be to find the time-dependent wave function for this system D(T,0,4,t). While you may use integral solvers or tables to help you with this problem you must show your work here of the setup and take some steps to simplify it before resorting to a solver. Simply jumping from the initial integral to the final answer is not sufficient.]

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