ABSTRACT
The purpose of this chapter is to argue that rather a combination of the two methods, to be called ergodic quantization from now on, will render good quantitative predictions in the field of quantum chaos. It starts by shortly reminding the reader how ergodic quantization works for the well known case of the spectrum. Next, an analogous treatment is developed for the matrix elements of operators in the energy representation (the representation in which the Hamiltonian is diagonal). The chapter looks at some methods by which semiclassical information about matrix elements of generic operators in the energy representation can be obtained. The matrix elements of operators are analyzed in the eigenvector basis. A predictive method is devised for the matrix elements in the energy representation which is partly exact and partly statistical.
