6.C: The Pauli principle
There is one slight catch before we finish the story on helium, the Pauli principle. This is another requirement of quantum mechanics which has no classical analog. The Pauli principle requires that electrons, when moving as independent particles, all use different wave functions. Superficially, it looks like our wave function for helium violates the Pauli principle. However, we have yet to specify the spin quantum number of the two electrons. If we put m_s = 1/2 for one electron and m_s = -1/2 for the other, then the Pauli principle is indeed satisfied. The helium wave function in this form is often referred to in abbreviated notation as ``1s squared''.