Semiclassical quantization of Kowalewski top

It is shown that the quantum analogue of the Kovalevskaya top found recently by Dorizzi et al. is equivalent to that found by Lapporte still in the early thirties. Leading terms of the asymptotics of the quantum spectrum in weak and strong fields are derived. The Hamiltonian structure of the Kovalevskaya equations is restored. The action of the system is obtained by means of separation of variables in the Hamiltonian. The quasiclassical quantization condition is solved numerically by direct computation as well as by the adiabatic switching method. The results are presented as functions of the field strength.