Multiparticle Quantum Systems in Constant Magnetic Fields

Christian Gérard, Izabella Łaba

Fundamentals Geometrical methods I The Mourre theory Basic propagation estimates Geometrical methods II Wave operators and scattering theory Open problems Appendix Bibliography Index.

Philip R. Wallace

Vladimir V. Lugovoi

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.

Eric L. Michelsen

Timothy H Boyer

The classical electromagnetic interaction of a point charge and a magnet is discussed by first calculating the interaction of a point charge with a simple model magnetic moment and then suggesting a multiparticle limit. The Darwin–Lagrangian is used to analyse the electromagnetic behaviour of the model magnetic moment (composed of two oppositely charged particles of different masses in an initially circular Coulomb orbit) interacting with a passing point charge. Considerations of force, energy, momentum and centre of energy are treated through second order in 1/ c . The changing magnetic moment is found to put a force back on a passing charge; this force is of order 1/ c 2 and depends upon the magnitude of the magnetic moment. The limit of a many-particle magnet arranged as a toroid is discussed. It is suggested that in the multiparticle limit, the electric fields of the passing charge are screened out of the body of the magnet while the magnetic fields of the passing charge penetrate into the body of the magnet. This is consistent with our understanding of the penetration of electromagnetic velocity fields into ohmic conductors. The proposed multiparticle limit is consistent with the conservation laws for energy and momentum, as well as constant motion of the centre of energy, and Newton's third law for the net Lorentz forces on the magnet and on the point charge. The work corresponds to a classical electromagnetic analysis of the interaction which is basic to understanding the controversy over the Aharonov–Bohm and Aharonov–Casher phase shifts and represents a refutation of the suggestions of Aharonov, Pearle and Vaidman.

V. I. Skrypnik