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In atomic physics, the central field approximation for many-electron atoms takes the combined electric fields of the nucleus and all the electrons acting on any of the electrons to be radial and to be the same for all the electrons in the atom. That is, every electron sees an identical potential \( {\displaystyle U(r)} \) that is only a function of its distance from the nucleus.

This facilitates an approximate analytical solution to the eigenvalue problem for the Hamiltonian operator.

s-type drum modes and wave functions

Drum mode ${\displaystyle u_{01}}$

Drum mode ${\displaystyle u_{02}}$

Drum mode ${\displaystyle u_{03}}$

Wave function of 1s orbital (real part, 2D-cut, ${\displaystyle r_{max}=2a_{0}}$)

Wave function of 2s orbital (real part, 2D-cut, ${\displaystyle r_{max}=10a_{0}}$)

Physics Encyclopedia

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