QUASI-CLASSICAL SPECTRAL SERIES OF SCALAR AND MATRIX OPERATORS IN QUANTUM MECHANICS CORRESPONDING TO NON-INTEGRATED HAMILTONIAN SYSTEMS WITH SYMMETRIE

The quasi-classical spectral series for some multidimensional classical-non-integrated Hamiltonians have been constructed on base of the method of canonic Maslov operator with complex phase. The new spectral series (of Schroedinger operator) for classical-non-integrated model - system of two connected non-linear oscillators and anisotropy Kepler problem in the homogeneous magnetic field have been found. For last model the spectral series (of Pauli, Klein - Gordon and Dirac operators) taking the electron spin and also relativistic effects into consideration have been constructed firstly. For pair of connected non-linear oscillators, the constructed quasi-classical spectral series are uniform according to the classical problem parameter incoming into the potential. The obtained formulae for quasi-classical spectral series of the Schroedinger, Pauli, Klein - Gordon and Dirac operators can be used in the quantum mechanics, theoretical and mathematical physicsAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio