Introduction
The Hamiltonian of helium, considered as a three-body system of two electrons and a nucleus and after separating out the centre-of-mass motion, can be written as
where is the reduced mass of an electron with respect to the nucleus, and are the electron-nucleus distance vectors and . The nuclear charge, is 2 for helium. Consider so that and the mass polarization term disappear. The Hamiltonian in atomic units (a.u.) for simplicity is given by
The presence of the electron-electron interaction term 1/r12 makes this equation non separable. This means that can't be written as a single product of one-electron wave functions. This means that the wave function is entangled. Measurements cannot be made on one particle without affecting the other. This is dealt with in the Hartree-Fock and Thomas-Fermi approximations.
Read more about this topic: Helium Atom
Famous quotes containing the word introduction:
“We used chamber-pots a good deal.... My mother ... loved to repeat: “When did the queen reign over China?” This whimsical and harmless scatological pun was my first introduction to the wonderful world of verbal transformations, and also a first perception that a joke need not be funny to give pleasure.”
—Angela Carter (1940–1992)
“For better or worse, stepparenting is self-conscious parenting. You’re damned if you do, and damned if you don’t.”
—Anonymous Parent. Making It as a Stepparent, by Claire Berman, introduction (1980, repr. 1986)