Determination of the energy of electron in a quantum wire with a point defect

A problem of finding the energy of ground state of a quantum particle in a nanostructure with axial symmetry is considered. It is assumed that there is a point defect inside the nanostructure, which is given by δ-potential. A transcendent equation, which defines the lowest level of energy of the particle, is obtained. Corresponding formulas are used for calculation of the threshold frequency of interband absorption of light in semiconductor nanocrystals, which are dispersed in transparent dielectric matrix. Absorption spectrum edge dependence on location and power of δ-potential is obtained. It is shown that the effective length of the cylindrical nanocrystal is decreased in case of existence of δ-potential, which leads to increase in the threshold frequency of the optical spectrum of absorption.