Problem of Molecular Vibrations with the Gaussian Potential

Abstract

The choice of the form of a potential function in calculating the characteristics of stationary states for atomic vibrations in a molecule is discussed. With regard to the features of the purely Coulomb potential and general considerations on the stable states of a bound nucleus set, and also a decrease in distances between the energy levels with increasing excitation energies, it is proposed to use a potential in the form of the “overturned” multidimensional Gaussian. It is demonstrated that this problem is solved by a variational procedure in the basis of products of one-dimensional functions forming a complete set.