(Solution) - a Apply the generalized Hellmann Feynman theorem with Z as the -(2025 Original AI-Free Solution)

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(a) Apply the generalized Hellmann-Feynman theorem with Z as the parameter to find (1/r) for the hydrogen like-atom bound states (nlm.
(b) Since hydrogen like functions (nlm with the same n but different l or m have the same energy, we must be sure that the functions (nlm are the correct zeroth-order functions for the perturbation of varying Z. Use a theorem of Section 9.6 to verify this.