Natural Science Forum / Physics / Relativity / May 2006

I'm sorry, none of that made any sense whatsoever. Would you care to
try again, or do you want me to have a go?

PD

chemguy:

 Don't be silly. The hamiltonian for the helium atom is,

H = [(p_1)^2 + (p_2)^2]/2m - 2e^2 [(1/r_1) + (1/r_2)]

            + e^2/|\vec{r_1} - \vec{r_2}| + screening
           
            + spin-orit + spin-spin terms

 You can most likely find it any basic quantum mechanics textbook,
with the screening, spin-orbit and spin-spin terms treated with
whatever level of sophistication was presumed of the audience for
which the book was intended.

 Just because the solution to the differential equation cannot be
given in a simple closed form doesn't mean the there are no eigenvalues.
Furthermore, not knowing the prcise form of the potentials (such as
the screening term) does not invalidate the theory. If one required an
exact solution in closed form or some a priori clairvoyance as to the
form of the potentials, as criteria for correctness, newtonian physics
would have been dead in the water before newton published the principia.
Obviously, there are no real physical problems for which newton or anyone
since could have obtained solutions in closed form. If you think there
are, name one.

 Basically, you need to look at an introductory quantum mechanics
textbook. One may obtain solutions of the above hamiltonian in a
rather straightforward way. First, find the ground state wavefunctions
neglecting the electron-electron interaction term (in which case, the
hamiltonian is separable), then treat the electron-electron interaction
and screening in perturbation theory.