Atomic orbitals spdf m-eigenstates and superpositions

Autor:

Geek3

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https://czwiki.cz/b/8df6e

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Collection of 16 atomic single-electron orbitals for the lowest four n quantum numbers. Only the cases ${\displaystyle n=l+1}$ with one radial node are shown. Each row shows one l-quantum number l=0 (s), l=1 (p), l=2 (d) and l=3 (f). The color depicts the complex-valued phase of the wavefunction. The right half depicts m_z-eigenstates with m quantum numbers ${\displaystyle m\in \{0,\ldots ,l\}}$ in ascending order showing complex phases and probability densities which are symmetric around the z-axis. The left half shows real-valued superpositions of ±m, which break the rotational symmetry and are often used in chemistry. The solid bodies enclose the volume where the continuous probability density exceeds a well-chosen threshold. The formulas that describe the orbitals can be found at Hydrogen atom.
The labels in the image show the quantum numbers nl_m with l encoded as letter and m replaced by the spatial alignment for the real-valued superpositions.

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CC BY-SA 4.0

Credit:

Vlastní dílo, Created with hydrogen 1.1

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