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 wave function is expressed as a product of radial and angular components, where the radial part R nl(r) is given using Laguarre polynomials and the angular part Yl m(θ,ϕ) is given by the spherical harmonics, which are expressed in terms of associated Legendre pokynomials Plm(cos θ). The general form of the angular part of the hydrogen wave function is:
Ylm(θ,ϕ) =
where
This simulation plots the (x,z) projection of the angular part of the hydrogen wave function Ylm(θ,0) to display 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/>.