Lugovoi V.V. One-Dimensional Filamentary Multiparticle Quantum Structures Arising in the Plane Transverse to External Homogeneous Magnetic Field. Copyright © 2015 by author and Scientific Research Publishing Inc.

Abstract It is shown  that a single-particle wave function Ψ, obtained (Landau, 1930) as a  solution of the Schrödinger equation (for a charged particle in a homogeneous magnetic  field), and an operator relation of p mv =   (or equation ΨΨ d dxpmt) lead to the  dynamic description of one-dimensional many-particle quantum filamentary states. Thus, one can overcome the problem, connected with the finding of many-body wave function as solution of the Schrödinger equation with a very tangled Hamiltonian  for multi-body system. An effect of nonlocality appears. The dependence of the  linear density of particles on the magnetic field and on the number of particles in the one-dimension filamentary multiparticle quantum structure is calculated.