  Energy level structure and direct light absorption in a cylindrical quantum
dot, having thin falciform cross section, are studied within the framework of
the adiabatic approximation. An analytical expression for the energy spectrum
of the particle is obtained. For the one-dimensional fast subsystem, an
oscillatory dependence of the wave function amplitude on the cross section
parameters is revealed. For treatment of the slow subsystem, parabolic and
modified Poschl-Teller effective potentials are used. It is shown that the
low-energy levels of the spectrum are equidistant. In the strong quantization
regime, the absorption coefficient and edge frequencies are calculated.
Selection rules for the corresponding quantum transitions are obtained.
