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 ψnlm(r,θ,ϕ)= Rnl(r)Yl 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 Yl m(θ,ϕ) is given by the spherical harmonics, which are expressed in terms of associated Legendre polynomials Plm(cos θ).
The general form of the angular part of the hydrogen wave function is:
where
This simulation plots the (x,z) projection of the angular part of the hydrogenic wave function Ylm(θ,0) to show the spatial orientation of the electron's orbital around the nucleus. Because the projection of the orbital angular momentum along z-axis cannot be larger than the value of l, the m quantum number can only take on the values -l, -l+1, ... , -2, -1, 0, 1, 2, ... , l-1, l.
The EJS JavaScript version of this simulation was developed by Wolfgang Christian from the original Java version. This Java is also available in the ComPADRE OSP Collection.
Information about EJS is available at: <http://www.um.es/fem/Ejs/>.