3. Consider a hydrogen atom that is in the following superposition ...

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3. Consider a hydrogen atom that is in the following superposition of its energy eigenkets Jnlm > at c - 0 - (a) Calculate the normalization constant N and write down the normalized time-dependent state vector >. (b) If you measure the energy, what are the possibilities and what are the probabilities? Calculate the expectation value of the energy. Calculate the uncertainty in the energy ΔH. (c) If you measure L2, what are the possibilities and what are the probabilities? Calculate the expectation value of L?. Calculate the uncertainty in the total angular momentum ΔL?. (d) If you measure Lz, what are the possibilities and what are the probabilities? Calculate the expectation value of Lz.. Calculate the uncertainty in the angular momentum along Z ΔL2

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