Vasylevs'ka Y. Exactly solvable quantum potential models of spin and soliton origin

The objects of study: spin-gamiltonians for easy-axes paramagnets in a magnetic field, soliton solutions of the Korteveg-de-Friz equation. The aim of study: to find and to apply new classes of the exact solutions of Schrodinger equation with the simple explicit expressions for potentials, energy levels and wave-functions of stationary states. Methods and equipment: the method of a spin-coordinate correspondence, the method of chain fractions. New results: new classes of exact solutions of Schrodinger equation are found, for which the energy levels and wave functions in a simple explicit way were obtained. It turns out that the maximum of susceptibility for easy-axes paramagnets in a perpendicular magnetic field may have two pikes. For the first time the different local models of soliton origin by the quantum mechanical way are considered in detail, the formulae for corresponding wave functions are obtained.