# test3c - Physics 463 Final Exam Work all ve problems on...

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Physics 463 - Final Exam Work all f ve problems on this exam. You have until 4:30PM of the day after you receive this exam to complete it and turn it in. 1. Use the variational principle to f nd an appropriate bound for the f rst excited state energy ( n =2 )o fthe hydrogen atom, using a variational wave function of the form ψ ( r )= Ae α r Y 0 1 ( θ , φ ) , treating the positive constant α as a variational parameter. Explain why this bound applies most directly to the energy of the n =2 level, and is not appropriate for estimating the n =1 ground state energy. 2. A particle moving in one dimension is con f ned to the region x [0 ,L ] by an in f nite one-dimensional square well potential. It is initially in its ground state (at t = −∞ ) when a pulsed perturbation of the form V = V 0 cos( π x/L ) e t 2 / τ 2 is applied to the system. Find, using f rst order time dependent perturbation theory, the probabilty that the pulse causes the system to make a transition to the f rst excited state. How small must V 0 be in order for the f rst order result to be valid? 3. The total angular momentum of a particle with spin s = 1 2 is the sum ~ J = ~ L + ~ S of its orbital and spin

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test3c - Physics 463 Final Exam Work all ve problems on...

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