Iterative Method for Solution of the One-Dimensional Wave Equation: Eigenvalues and Eigenfunctions for L-J (12, 6) and Exponential (α, 6) Interatomic Potentials

A method of direct numerical integration of the one-dimensional wave equation is described and illustrated by calculations of the radial wavefunctions, vibrational energy levels, and numbers of bound states for diatomic molecules. Within the validity of the Born—Oppenheimer approximation, the procedure yields arbitrarily accurate eigenvalues. Several potentials involving long-range, inverse-sixth-power attractions are examined. Results are compared with those from the first-order WKBJ integral and with the Dunham form of the second-order WKBJ approximation.