Introduction to Quantum Mechanics · Problem 8.15

The Variational Principle — David J. Griffiths

Physics — Quantum Mechanics · hydrogen_molecule_energy

Problem

Make a plot of the kinetic energy for both the singlet and triplet states of H2_2, as a function of R/aR/a. Do the same for the electron-proton potential energy and for the electron–electron potential energy. You should find that the triplet state has lower potential energy than the singlet state for all values of RR. However, the singlet state's kinetic energy is *so* much smaller that its total energy comes out lower. *Comment:* In situations where there is not a large kinetic energy cost to aligning the spins, such as two electrons in a partially filled orbital in an atom, the triplet state can come out lower in energy. This is the physics behind Hund's first rule.

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