A ferromagnetic crystal with a simple cubic lattice and an arbitrary spin containing a plane defect is considered. The possibility of the formation of two-magnon states localized on a defect dislocation is analyzed and proved.

An over-complete set of coherent states in the trajectory parametrization is built for a many-dimensional system with a Hamiltonian quadratic in momenta and coordinates. This parametrization enables us to solve consistently the problem of the vacuum state in the coherent state system. The...

Quantum corrections for the equilibrium distribution function of a system of charged particles interacting with arbitrary nonuniform magnetic and potential fields are found up to the fourth power of Planck's constant. The free energy and the magnetic moment of the system are calculated with the...

Explicit expressions for the Green functions of arbitrary relativistic quadratic quantum systems are obtained by the integrals-of-motion method and by the coherent states method. The normal forms of the relativistic quadratic hamiltonians are briefly discussed. The important special cases, such...

We obtain the explicit expressions for phase space eigenfunctions (PSE), i.e. Weyl's symbols of dyadic operators like |n <m|, |n >, |m being the solution of the Schrödinger equation with the Hamiltonian which is a quite arbitrary multidimensional quadratic form of the operators of Cartesian...</m|,>

We analyse and compare the properties of the integrals of motion of two types of quantum systems: pure systems which can be described in terms of the wave functions obeying the Schrödinger equation and mixed systems described in terms of density matrix. The model equation for the Wigner...

We propose a new class of nonlinear homogeneous extension of the Doebner-Goldin Schrödinger equation, valid for arbitrary representations and operators, chosen in accordance with the investigated physical problem. We verify that the nonlinearity simulates an environment, thence, the new model...

We calculate the response of a two-level system to a monochromatic excitation in the framework of a nonlinear homogeneous dissipative generalization of the Schrödinger equation. Non-Lorentzian dependences of the real and imaginary parts of the dynamical response function on the frequency are...

The explicit expressions for the Green functions of quantum systems with nonstationary Hamiltonians which are general quadratic forms with respect of coordinates and momenta are obtained in the mixed (Wigner's) representation.