3D Hydrogen Atomic Orbital Visualizer

Equation Notes

• This is the spatial wavefunction \(\psi(r, \theta, \phi)\) of a hydrogen-like atom. The radial distance \(r\) is expressed in units of the Bohr radius \(a_0\).
• The radial part \(R_{nl}(r)\) is constructed from the corresponding generalized Laguerre polynomials \(L_n^\alpha(x)\).
• The angular part is expressed using real spherical harmonics \(Y_{lm}(\theta, \phi)\), rather than the complex form. This makes the resulting orbital shapes directly correspond to familiar chemical orbitals such as \(p_x\), \(p_y\), and \(d_{xy}\).