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with eigenvalues and eigenfunctions, respectively:. the eigenfunctions Ψ represent orbitals and describe the bound states of one-electron atoms, while | Ψ | 2 represents the probability density of finding the electron at the position ( r ,θ,φ ). cannot be solved analytically !.
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with eigenvalues and eigenfunctions, respectively: the eigenfunctions Ψ represent orbitals and describe the bound states of one-electron atoms, while |Ψ|2 represents the probability density of finding the electron at the position (r,θ,φ)
cannot be solved analytically ! not compatible with Pauli principle spin-orbital Slater determinant represents suitable N-electron wavefunctions that fulfill the Pauli principle for fermions
2 electrons in the same spin-orbital forbidden! 2 unpaired electrons => no restriction by Pauli principle (electrons in different orbitals ) electrostatic repulsion=> energetic splitting => Triplet and Singlet state 4 antisymmetrised functions fulfilling the Pauli principle result: Triplet state lies lower in energy than the Singlet state
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