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written by
Wolfgang Christian *

This simulation plots the (x,z) projection of the angular part of the hydrogenic wave function *Y*_{l}^{m}(θ,0) to show the spatial orientation of the electron's orbital around the nucleus.

The hydrogenic wave function is a solution to the Schrödinger equation for an idealized hydrogen atom. It describes the probability amplitude of finding an electron in a particular state defined by quantum numbers

*n*, *l*, and *m*. The complete wave function ψ_{nlm}(r,θ,ϕ)=

*R*_{nl}(r)*Y*_{l}

^{m}(θ,ϕ) is expressed in spherical polar coordinates as a product of radial and angular components, where the radial part *R*

_{nl}(r) is expressed using Laguerre polynomials and the angular part *Y*_{l}

^{m}(θ,ϕ) is given by the spherical harmonics, which are expressed in terms of associated Legendre polynomials *P*_{l}^{m}(cos θ).

Published *March 13, 2024*

Last Modified *March 29, 2024*

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