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
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