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Consider the H− ion (1 protons and two electrons). Apply the variational technique employed in the Helium
atom, to determine the ground state energy of this system and the effective (partially screened) charge

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iii) Consider a 2D square potential energy well with sides L (length) containing six electrons. The potential energy is infinite at the sides and zero inside. The h? single-particle energies are given by 8mL +n), where n and ny are integers. If a seventh electron is added to the system when it is in its ground state find the least energy the additional electron can have?
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I have put 1.37, 1.49, 1.50, 1.3, 1.3 x 10^-3 All have been wrong, I need help with (a).
Model the effective potential seen by the least bound proton in the nucleus as a square well with depth Bn inside the nuclear radius R, plus a repulsive Coulomb potential from a uniform charge distribution of the other protons inside the nucleus. Estimate Br for 209 Bi (mass number A = 209 and atomic number Z = 83), the largest stable isotope. How is Bn related to the depth of the nuclear potential Vo? Hint: The electrostatic potential a distance r from the center of a uniformly charged sphere of radius R and total charge Q is given by: for r < R. Q V = (3R² — r²) 8πTEOR³
Show that the commutator [ô, ô] - 28. 2i XI

Consider the H− ion (1 protons and two electrons). Apply the variational technique employed in the Heliumatom, to determine the ground state energy of this system and the effective (partially screened) charge