Path Integrals and Semiclassical Tunneling, Wavefunctions, and Energies

The semiclassical limit of Feynman path integrals is investigated in order to determine those classical trajectories which contribute to tunneling processes. The semiclassical bound state energies, wavefunctions, and scattering phase shifts are directly recovered from the poles and residues of the semiclassical Green's function in energy space. Some extensions to cases of tunneling and bound states for multidimensional nonseparable potentials are discussed.