2. Polyelectronic systems
2.1 General
The hydrogen atom and the molecular ion are the only two systems whose eigenstates are known exactly. For all other systems, we obtain Hamiltonians containing electrostatic electron-electron interaction terms that make it impossible to solve Schrödinger's equation analytically. Such a phenomenon is very common in physics, as static systems of interacting particles generally admit no simple solutions due to inter-particle interaction terms.
We must therefore abandon the usual mathematical arsenal of eigenfunctions and eigenvalues of the Hamiltonian and replace...
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Polyelectronic systems
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