Abstract. Qualitative features of the Manakov top are discussed for the classical and quantum versions of the problem. Energy-momentum diagram for this integrable classical problem and quantum joint spectrum of two commuting observables for associated quantum problem are analyzed. It is demonstrated that the evolution of the specially chosen quantum cell through the joint quantum spectrum can be defined for paths which cross singular strata. The corresponding quantum monodromy transformation is introduced. Personal introductionIt was about six years ago that I (B.Z.) met for the first time Vadim Kuznetsov during one of the 'Geometric Mechanics' conferences in Warwick University, U.K. I cannot say that we have found immediately mutual interest in our research works in spite of the fact that our problems were rather related. At that time I tried to understand better the manifestation of classical Hamiltonian monodromy in corresponding quantum problems and looked for different simple classical integrable models with monodromy which could be of interest for physical, mainly molecular, applications. Vadim worked on much more formal mathematical aspects of integrable models related to almost unknown for me special functions. I tried to convince him that from the point of view of physical applications the most important task is to understand qualitative features of integrable models using some simple geometric tools like classification of defects of regular lattices formed by joint spectrum of several commuting observables. Vadim insisted on special functions, complex analysis, Lie algebras etc. Nevertheless, we have found many points of common interest. Soon after, Vadim visited Dunkerque and we have tried to find some concrete problem, where we could demonstrate clearly what each of us means by understanding the solution. In fact, such problem was found quickly. It was the Manakov top. Vadim was interested in Manakov top because of its relation with XYZ Gaudin magnet. He published a short paper together with I. Komarov on this subject in 1991 [16]. For me the model problem like Manakov top represented certain interest because it is naturally related to molecular models constructed, for example, by coupled angular momenta or by angular momentum and

UDC 539.194We realized the method for determining the potential function of the segregated electron state of a polyatomic molecule from experimental data using a hydrogen selenide molecule as an example. Dependences of various spectroscopic parameters on the parameters of the potential function in the natural coordinates were studied. From the obtained data, the potential function of the hydrogen selenide molecule was reconstructed up to the fourth order of smallness.

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