Exactly soluble two-electron atomic model
Abstract
For the class of ``heliumlike'' Hamiltonians, H=- 1/2 ∇21 - 1/2 ∇22 +V(r1)+V(r2)+W(r12), there is a fortuitous choice of (attractive) V and (repulsive) W potentials such that the system admits of exact analytic solution in both classical and quantum pictures. Specifically, harmonic attraction and inverse-cube repulsion forces result in a soluble three-body problem (with infinite nuclear mass). We derive the general classical electron trajectories and give a complete set of eigenfunctions of the Hamiltonian. We indicate how exact expectation values can be obtained and show that best fits to actual helium data require a nonzero repulsive coupling constant. We exhibit an s-state basis subset of wave functions, suitable for application to general problems of atomic and chemical physics.
- Publication:
-
American Journal of Physics
- Pub Date:
- May 1984
- DOI:
- 10.1119/1.13650
- Bibcode:
- 1984AmJPh..52..438C
- Keywords:
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- 31.15.+q;
- 03.65.Ge;
- Solutions of wave equations: bound states