Solving the Problem of Electron-Vibrational-Rotational Energy Levels of a Polyatomic Molecule of Arbitrary Structure in Generalized Coordinates

Abstract

In classical mechanics, the problems of the motion of objects with many degrees of freedom are formulated and solved using generalized coordinates rather than Cartesian coordinates. It is shown that a similar approach is also applicable to quantum mechanics. In both cases, the problem statement requires introduction of the potential function in appropriate coordinates and construction of the matrix of kinematic coefficients as a part of the classical expression of kinetic energy in the momentum representation. The possibility of the same problem statement is consistently discussed for the energy levels of polyatomic molecules. Some examples of its solution using generalized coordinates are provided.