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

Author(s)
Vladimir V. Lugovoi

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.

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.

KEYWORDS

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

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

Cite this paper

Lugovoi, V. (2015) One-Dimensional Filamentary Multiparticle Quantum Structures Arising in the Plane Transverse to External Homogeneous Magnetic Field.*Journal of Modern Physics*, **6**, 990-1003. doi: 10.4236/jmp.2015.67103.

Lugovoi, V. (2015) One-Dimensional Filamentary Multiparticle Quantum Structures Arising in the Plane Transverse to External Homogeneous Magnetic Field.

References

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[1] Landau, L.D. and Lifshitz, E.M. (1974) Quantum Mechanics. Nauka, Moscow City.

[2] Blokhintsev, D.I. (1976) Foundations of Quantum Mechanics. Nauka, Moscow City.

[3] Wichmann, E.H. (1971) Quantum Physics. Berkeley Physics Course. McGraw-Hill Book Company.

[4] Landau, L.D. and Lifshitz, E.M. (1965) Mechanics. Nauka, Moscow City.

[5] Einstein, A. (1965) Physics and Reality. Nauka, Moscow City.

[6] Chudakov, V.M. (2010) Physical-Technical Institute of Uzbek Academy of Science. Tashkent. Report No.011.

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

[8] Feynman, R.P. and Hibbs A.R. (1968) Quantum Mechanics and Path Integrals. Mir, Moscow City.

[9] Fikhtengoltz, G.M. (1956) Principles of Mathematical Analysis. Nauka, Moscow City.

[10] Dwight, H.B. (1961) Tables of Integrals and other Mathematical Data. The Macmillan Company, New York.

[11] Artsimovich, L.A. and Lukyanov, S.Yu. (1972) The Moving of Charged Particles in the Electric and Magnetic Fields. Nauka, Moscow City.

[12] Lugovoi, V.V. (2013) United Quantum Oscillator. Molecular Bond, Graphene, Plasma, Fusion. LAP Lambert Academic Publishing, Saarbrucken.