Energies of the ground and some excited states of on-centre donors in spherical quantum dots are calculated, within the effective mass approximation, as functions of the R dot radius and for different potential shapes. We propose an exact numerical solution for the radial Schrödinger equation in a quantum dot with any arbitrary spherical potential by using a trigonometric sweep method. An evident increase in the binding energy is found as the soft-edge-barrier potential model is considered. It is found that the binding energy increases as the dot size decreases up to a dot radius critical value and then, for R slightly smaller than , the impurity wave function spreads to the barrier region and the 3D character is rapidly restored. The properties of the shallow donors in a quantum dot with a double-step potential barrier and multiple barriers are analysed, and two peaks in the binding energy are found. Our results for the spherical-rectangular potential are in good agreement with previous calculations obtained using other methods.

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A theoretical investigation has been made of the dependence of the shape and breadth of the absorption band for stretching vibrations V O H in hydrogen bonds of an alcohol crystal on the concentration of an isotopic impurity. It is shown that the structure of the V O H band is caused by Davydov splitting. The local mode frequencie8 arising 011 deuteration of an individual alcohol molecule are calculated using the Green's function method and the introduction of such impurity molecules into the crystal is found to lead to an effective drsintegration of the hydrogen-bonded chain to shorter chains. A method is proposed of constructing the absorption V O H band contour. The V O H absorption band contour is constructed for various concentrations of deuterated molecules under the assumption of their random distribution. The splitting of the V O H doublet decreases with increasing concentration of deoterated molecules, owing to the effective decrease of the lengths of the chain formed by hydrogen bonds in an alcohol crystal. QJIH KpHcTanna cnHpTa TeopeTwrecm m y s e~a ~~B H C M M O C

We reduce the problems of the on-and off-center D 0 and D --S-states in semiconductor heterostructures to the similar ones in an isotropic effective space with variable fractional dimension starting from the variational principle. The dimension of this space is defined as a scaling parameter that relates the radii of a set of spherical boxes to the charge densities within induced by the free electron ground state in the heterostructure. Explicit expressions for the effective space dimensionality in a quantum well (QW), quantum-well wire (QWW) and a quantum dot (QD) are found by using this definition. To solve the wave equations for the free electron ground state in the heterostructure and for the hydrogen-like atom S-states in the fractional-dimensional space, we use the numerical trigonometric sweep method. The three-parameter Hylleraas trial function is used to solve the similar problem for a negative-hydrogen-like ion in the effective space. Ground state binding energies for off-center neutral and negatively charged donors in QWs and spherical QDs are calculated. Our results are in a good agreement with those of the variational and Monte Carlo methods. In addition, novel results for the D --binding energy as a function of the cylindrical GaAs/Ga 0.7 Al 0.3 As QWW radius and the magnetic field intensity are presented. It is found that the D --binding energy in the wire increases from 0.055 Ry * up to about 1.230 Ry * as the radius decreases to 30 A. It is also shown that the magnetic field produces a considerable enhancement of negative-donor binding energy in QWW only for radii greater than 100 A.

We analyze the effect of the mixing of the 1s and 2p x,y subbands on the ground state binding energy of the off-axis donors in cylindrical nanotubes by using the recently developed fractal dimension method. Curves of the D 0 ground state binding energies as a function of the donor distance from axis are presented and compared with those obtained previously without consideration of the effect of the subband mixing. Also, we analyze the density impurity states in nanotubes with randomly distributed donors.