One-dimensional realization of the SU(2) group and its role in nuclear physics

One-dimensional realizations of the SU(2) group with a complex variable are built to describe coherent states of both integer and half-integer angular momenta. The problem of obtaining a wave function of a summary momentum without Clebsch-Gordon coefficients is solved. Representation based on polynomials of complex variables a particular case of which is representation of the SU(2) group permits to develop a method for hamiltonian solution, describing collective nucleus motion. The method is based on using a quasi-classical approximation in a complex plane. A problem on rotation of a quantum nonsymmetrical gyroscope is solved by the method developed, phase transformations in a nucleus are described