Decay Rate of Energy Eigenfunctions in Classically Energetically Inaccessible Regions

Classically energetically inaccessible parts of energy eigenfunctions in configuration space are studied by making use of a generalization of Brillouin--Wigner perturbation theory. Approximate formulas are proposed for describing local decaying rate of this part of energy eigenfunctions, which are useful in the study of quantum phenomena,such as tunnelling effect, and are tested in an anharmonic oscillator.