In the descritption of the atom by the hamiltonian transpose by quantum operators into a generalized Shrödinger equation of the n-body problem of a nucleon with n electrons that have mutual interractions of electrostatic type. What are the methodologies to solve such problem? And does the Bohr-Oppenheimer approximation gives analytical solutions?
If we consider the böhr-Oppenheimer approximation. We can build the n-body Schrodinger equation wave function vectorial space as the tensorial product of the two-body (proton-electron) wave functions vectorial spaces. But only if we neglect the mutual influence of the electrons between them. I invite the reader to see the application of this principle in the frame of my article on quantum gravity and the n-body problem. Then we can add the mutual influence between electrons by a perturbation method solution.
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