Single-particle states and interband optical transitions in radially-symmetric semiconductor heterolayers

With the use of WKB (Wentzel–Kramers–Brillouin) method the quantum-mechanical problem of single-particle states in semiconductor quantized cylindrical and spherical layers is solved. Explicit analytical dependences of the energy spectrum and wave functions of charge carriers on geometrical sizes of the system and quantum numbers of radial and orbital movements of the particles are obtained. The results of analytical solution are compared with the results of numerical calculations. The results obtained are used to calculate coefficients of interband optical absorption in cylindrical and spherical heterolayers.