A new approach to the theory of anisotropic exciton based on Fock transformation, i.e., on a stereographic projection of the momentum to the unit 4-dimensional (4D) sphere, is developed. Hyperspherical functions are used as a basis of the perturbatio
n theory. The binding energies, wave functions and oscillator strengths of elongated as well as flattened excitons are obtained numerically. It is shown that with an increase of the anisotropy degree the oscillator strengths are markedly redistributed between optically active and formerly inactive states, making the latter optically active. An approximate analytical solution of the anisotropic exciton problem taking into account the angular momentum conserving terms is obtained. This solution gives the binding energies of moderately anisotropic exciton with a good accuracy and provides a useful qualitative description of the energy level evolution.
The theory of inelastic electron tunneling spectroscopy (IETS) and motions of single adsorbed atoms and molecules on metal surfaces induced by vibrational excitation with a scanning tunneling microscope (STM) is reviewed. The theory of STM-IETS is de
scribed using the adsorbate-induced resonance model. Elementary processes of how an adsorbate overcomes the potential barrier along the reaction coordinate (RC) by inelastic tunneling current are described with a focus on direct excitation of the RC mode by coherent and incoherent vibrational ladder climbing and an indirect one through anharmonic coupling to a mode excited by tunneling electrons. Action spectroscopy of single molecule motions is also discussed. The latter allows a direct access to the vibrational density of states, which can not be otherwise observed in the STM-IETS because of a competition between the elastic and inelastic tunneling currents.
