Solutions to Schrödinger’s equation

Abstract

Eigenstates of the square well potential are calculated and displayed. Barrier penetration and the connection to total internal reflection are explained. α‎–decay by barrier penetration is calculated and used to explain Geiger–Nuttall plots. Gauss–Hermite solutions to the harmonic oscillator potential are deduced and displayed. Zero point fluctuations are introduced. Hydrogen atom eigenstate wavefunctions for the Coulomb potential are calculated and displayed. Principal, orbital angular momentum and intrinsic angular momentum quantum numbers and their allowed combinations are discussed and interpreted: n, l, ml, s and ms. The Stern–Gerlach experiment and Pauli’s perception that electron spin is half-integral are presented; as are Beth’s experiment and photon spin. Dominance of electric dipole transitions and resulting selection rules discussed. Fine spectral structure and spin-orbit coupling are described. Nuclear spin and resulting hyperfine spectral structure are introduced. Landé factors introduced.