The purpose of this note is to verify that the inclusion of spin does
not change the spatial form of the ground state of the hydrogen
molecule. The lowest expectation energy
, characterizing
the correct ground state, only occurs if all spatial components
of the ground state with spin,
The reason is that the assumed Hamiltonian (5.3) does not
involve spin at all, only spatial coordinates, so, for example,
In addition, the wave function must be normalized,
1, or
It should be pointed out that to a more accurate approximation, spin causes the electrons to be somewhat magnetic, and that produces a slight dependence of the energy on spin; compare addendum {A.38}. This note ignored that, as do most other derivations in this book.