  The quantum states of the Kapitza pendulum are described within the effective
potential obtained by the method of averaging over the fast oscillations. An
analytical estimate of the energy spectrum of stabilized states is given using
approximate model potential. For the lowest states of an inverted pendulum, the
spectrum is repeduced by the energies of a harmonic oscillator with
perturbation theory corrections. Tunneling effect contribution to the energies
of resonance states in the double-well effective potential is estimated. The
results of numerical simulations of vibrational and rotational spectra of the
Kapitza pendulum by the semiclassical method and by the Numerov algorithm are
compared.
