arXiv subjects
Publications and source records attributed to V. P. Koshcheev.
It is shown that a chain of closed systems of first order ordinary differential equations describing the evolution of moments can be constructed using the Jacobi equation. It is shown that Wronsky determinants for fundamental matrices of closed systems of first order ordinary differential equations are integrals of motion on extremals of the Euler-Lagrange equation.
As part of a new approach to calculating the total energy of a diatomic molecule (cluster), it is shown that in the first order of perturbation theory, the total energy of a triatomic cluster is equal to the sum of the total energies of the diatomic clusters (molecules). If all three aluminum atoms are in the ground state of Al(2p), then the quantum of energy of collective electron oscillations (plasmon energy) in each of the diatomic clusters (molecules) is eV (electron volts).
In the first order of perturbation theory, the total energy of a diatomic molecule in the ground state is calculated taking into account the Pauli principle and plasma oscillations of atomic electrons. The Fourier component of the potential energy of interaction of an atom with an atom has the form of a polynomial of the fourth degree of the atomic form factor. Numerical calculation is performed for the atomic form factor in the approximation of hydrogen-like wave functions, which approximate the solution of the Hartree-Fock equation for an isolated atom. It is shown that taking into account the plasma oscillations of atomic electrons leads to a self-consistent system of equations, the numerical solution of which makes it possible to determine the elastic constant, that is, the value of the second derivative at the minimum of the potential energy of the molecule. The total energy for nitrogen and fluorine molecules is calculated.
An equation for the evolution of the energy of a dynamical system (Keldysh model with one degree of freedom), which contains a white noise source, is constructed. It is shown that self-oscillations (flutter) are suppressed if the intensity of white noise exceeds a critical value.