NUMERICAL METHODS FOR THE SOLUTION OF ONE-DIMENSIONAL OSCILLATOR PROBLEMS

Abstract

Numerical calculations of the vibrational stationary states of molecules have been found to be an important and useful approach to the study of unusual vibrational modes significantly unlike those of the harmonic oscillator. Recent computational studies of the hydrogen bond, for instance, have shown that particular approximations to the bound one-dimensional occillator problem can be applied with reasonable accuracy: G. R. Anderson and E. R. Lippincott, J. Chem. Phys. 55, 4077 (1971). A numerical recurrence equation approximation of the Schrodinger equation will be discussed, and a method will be outlined for approximating the wavefunction near the classical turning point of a bound oscillator.