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Sveshnikov, A.G. and Tikhonov, A.N. (1967) The Theory of Functions of Complex Variable. Nauka, Moscow City.

has been cited by the following article:

• TITLE: One-Dimensional Filamentary Multiparticle Quantum Structures Arising in the Plane Transverse to External Homogeneous Magnetic Field

  AUTHORS: Vladimir V. Lugovoi

  KEYWORDS: Quantum Mechanics, Trajectory of Quantum Ensemble, Quantum Turning Points, Many-Particle Filamentary States, Magnetic Field, Effect of Nonlocality, Linear Density of Particles

  JOURNAL NAME: Journal of Modern Physics, Vol.6 No.7, June 30, 2015

  ABSTRACT: It is shown that a single-particle wave function Ψ, obtained (Landau, 1930) as a solution of the Schr?dinger equation (for a charged particle in a homogeneous magnetic field), and an operator relation of(or equation) 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 Schr?dinger 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.