The Helium-4 Atom
The helium atom is the second simplest atom (hydrogen is the simplest), but the extra electron introduces a third "body", so that solution to its wave equation becomes a "three body problem", which has no analytic solution. However, numerical approximations of the equations of quantum mechanics have given a good estimate of the key atomic properties of helium-4, such as its size and ionization energy.
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“We have grasped the mystery of the atom and rejected the Sermon on the Mount.... The world has achieved brilliance without wisdom, power without conscience. Ours is a world of nuclear giants and ethical infants.”
—Omar Bradley (1893–1981)