Question: When Hylleraas began his calculations on helium, it was not known whether the isolated hydride ion H was a stable entity. Calculate the ground-state energy

When Hylleraas began his calculations on helium, it was not known whether the isolated hydride ion H¯ was a stable entity. Calculate the ground-state energy of H¯ predicted by the trial function (9.56). Compare the result with the ground-state energy of the hydrogen atom, -13.60 eV, and show that this simple variation function (erroneously) indicates H¯ is unstable with respect to ionization into a hydrogen atom and an electron. (More complicated variational functions give a ground-state energy of - 14.35 eV.)

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