Inhomogeneous Density and Energy Spectrum of Elementary Excitations of Electron Liquid of Conductors in Magnetic Field

Abstract

It is shown that the conventional theory of electron liquid in a magnetic field is based on the model that is incorrecting mathematically and contradicting to experiments. On the foundation of statistical mechanics that takes into account angular momentum conservation law is obtained the effective Hamiltonian of the electron liquid in a magnetic field that includes the quasielectrostatic potential proportional to the square of the magnetic field. As result, the electron liquid is inhomogeneous, and together with the homogeneous neutralizingbackground generates an electrostatic potential. The sum of these potentials is the residual potential that forms an energetically spectrum of elementary excitations of the electron liquid in the homogeneousmagnetic field. This spectrum is quasicontinuous, and itsbeginning issomewhat higher than the value of the potential energy at the boundary. The graph of the dependence of the density of states on energy has the form of a staircasewith horizontal steps.The density of states in the mean is proportional to the square root from energy.