Hydrogen Atom Radial Functions

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The eigenfunctions in spherical coordinates for the hydrogen atom are , where
and
are the solutions to the radial and angular parts of the Schrödinger equation, respectively, and
,
, and
are the principal, orbital, and magnetic quantum numbers with allowed values
, and
. The
are the spherical harmonics and the radial functions are
, where
is the
-order associated Laguerre polynomial and
is the Bohr radius. The left graphic shows the radial probability density
and the expectation value
, and the right graphic shows the radial function.
Contributed by: Porscha McRobbie and Eitan Geva (January 2010)
Open content licensed under CC BY-NC-SA
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"Hydrogen Atom Radial Functions"
http://demonstrations.wolfram.com/HydrogenAtomRadialFunctions/
Wolfram Demonstrations Project
Published: January 8 2010