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Consider a helium atom where both electrons are replaced by identical charged particles of spin1. Ignoring the motion of the nucleus, the Hamiltonian is [see attachment 1]
Construct an energy level diagram ( qualitatively ) for this "atom", when both particles are in the n=1 state, and when one particle is in the n=1 state and the other is in the state (nlm)=(200). Do this by treating the term in the Hamiltonian as a perturbation. Write out the space and spin wavefunctions for each level in terms of the single particle hydrogenic wavefunctions [phi]nlm spin wavefunctions [chi]s,msubs. Show the splitting qualitatively, and state the degeneracy of each level.
Construct an energy level diagram ( qualitatively ) for this "atom", when both particles are in the n=1 state, and when one particle is in the n=1 state and the other is in the state (nlm)=(200). Do this by treating the term in the Hamiltonian as a perturbation. Write out the space and spin wavefunctions for each level in terms of the single particle hydrogenic wavefunctions [phi]nlm spin wavefunctions [chi]s,msubs. Show the splitting qualitatively, and state the degeneracy of each level.
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