Chladni Figures and One-Electron Atoms

Chladni Figures and One-Electron Atoms: After showing how a double-minimum potential generates one-dimensional bonding, Professor McBride moves on to multi-dimensional wave functions. Solving Schrödinger’s three-dimensional differential equation might have been daunting, but it was not, because the necessary formulas had been worked out more than a century earlier in connection with acoustics. Acoustical “Chladni” figures show how nodal patterns relate to frequencies. The analogy is pursued by studying the form of wave functions for “hydrogen-like” one-electron atoms. Removing normalizing constants from the formulas for familiar orbitals reveals the underlying simplicity of their shapes.