Physics Asked by ThePhysicist on July 30, 2020
Any electron in an atom is described as a standing wavefunction in a potential well. In multielectron atoms, when an electron in any orbital beyond 1S² is described, is it the resultant of interference of all other wavefunctions or is it calculated as if it’s the sole electron in that atom?
Inn principle it should be solved as a many-electron system, i.e. the electrons should be described by a joint wave function $Psi_{s_1,...,s_N}(mathbf{r}_1,...,mathbf{r}_N)$. However, in practice the many-body problem is no less challenging in quantum mechanics than in classical one, so one would often use approximations, representing multi-electron states as combinations of single-electron orbitals. Since these belong to different electrons, there is no interference them, although they do need to be modified to accommodate the Pauli principle and the electron-electron Coulomb interactions.
Answered by Vadim on July 30, 2020
These are different electrons that are in different orbitals, all labelled by different quantum numbers and hence distinguishable. Therefore, they do not interfere.
You will still detect a higher charge density if you hover over at a position where more than one orbital has a maximum. But this is the result of the sum of the intensities $|psi_1|^2 + |psi_2|^2$ (incoherent) rather than sum of the wavefunctions (coherent -> interference) $|psi_1 + psi_2|^2$.
Answered by SuperCiocia on July 30, 2020
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