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MULTIPOLAR REPRESENTATION OF MAXWELL AND SCHRÖDINGER EQUATIONS: LAGRANGIAN AND HAMILTONIAN FORMALISMS: EXAMPLES

By V. M. Dubovik, B. Saha and M. A. Martsenyuk

Abstract

Development of quantum engineering put forward new theoretical problems. Behavior of a single mesoscopic cell (device) we may usually describe by equations of quantum mechanics. However if experimentators gather hundreds of thousands of similar cells there arises some artificial medium that one already needs to describe by means of new electromagnetic equations. The same problem arises when we try to describe e.g. a sublattice structure of such complex substances like perovskites. It is demonstrated that the inherent primacy of vector potential in quantum systems leads to a generalization of the equations of electromagnetism by introducing in them toroid polarizations. To derive the equations of motion the Lagrangian and the Hamiltonian formalisms are used. Some examples where electromagnetic properties of molecules are described by the toroid Let us remind a known thing that says ”it is impossible to introduce electrodynamics of matter in general ” (E. A. Turov, 1983). For example, different types of crystalline structures of matter lead to the alignment of one or other type of polarizations in the matter considered. So the necessity to introduce in the equations of high tensor polarizatio

Year: 1996
OAI identifier: oai:CiteSeerX.psu:10.1.1.305.7577
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