Recent developments in semiclassical mechanics: eigenvalues and reaction rate constants

A semiclassical treatment of eigenvalues for a multidimensional non-separable potential function and of the rate constant for a chemical reaction with an activation barrier is presented. Both phenomena are seen to be described by essentially the same semiclassical formalism, which is based on a construction of the total Hamiltonian in terms of the complete set of good action variables (or adiabatic invariants) associated with the minimum in the potential energy surface for the eigenvalue case, or the saddle point in the potential energy surface for the case of chemical reaction. (Auth.)