The differential cross section for an electron Raman scattering process in a semiconductor quantum well wire (QWW) and in a free-standing wire of cylindrical geometry involving phonon-assisted transitions is calculated for T = 0 K. A complete description of the phonon modes of cylindrical structures embedded in another material, including a correct treatment of the mechanical and electrostatic matching conditions at the surface, is presented. We consider the Fröhlich interaction to illustrate the theory for a GaAs/AlAs system. Electron states are considered to be confined within a QWW with finite and infinite potential barriers. We also assume single parabolic conduction and valence bands. The emission spectra are discussed for different scattering configurations and the selection rules for the processes are also studied. Singularities in the spectra are found and interpreted.

Confined Beryllium atom ground and first excited states electronic structures are calculated by the direct variational method, taking into account the system asymmetric nature of the trial wave function, adding a cutoff function to ensure confinement boundary conditions. The trial wave function is built up from hydrogenic functions, which constitute an adequate basis for energies calculation. Physicochemical properties such as kinetic energy, pressure, and polarizability are also calculated from energy results previously obtained to different confined radii. Using different variational parameters in each hydrogenic function, the energy approximation obtained is improved. Electronic configuration changes as we move toward the strong confinement region (small cavity radii) in function of its atomic number using impenetrable walls, this region was obtained for Z=4. This is a conclusion of this work. Another important result is that this method is computationally simpler and gives values inside the experimental precision. Aforementioned results are compared with other theoretical publications.