MODELING OF A MEDIUM WITH THE PROPERTY OF A PERFECT MIRROR FOR THE LIGHT AND SPIN 1/2 PARTICLES
Abstract
The geometry of Lobachevsky space is considered as a basis for modeling an effective medium. In Lobachevsky space, Maxwell's equations in the 3D complex Majorana - Oppenheimer formalism are solved exactly. The problem effectively reduces to one second-order differential equation. In the context of quantum mechanics, such an equation describes the motion of a particle in a potential field gradually increasing to infinity; a particle is reflected from the barrier. The geometry of Lоbachevsky space simulates a perfect mirror distributed in the space. The penetration depth of the field into the “medium-mirror” is determined by the frequency of an electromagnetic wave and by the curvature radius of an effective modeling space. The influence of the geometry on spin 1/2 particles is the same: the “medium” acts on fermions as a perfect mirror, the penetration depth of particles increases with energy and decreases with increasing the space curvature.
About the Authors
E. M. Ovsiyuk
Mozyr State Pedagogical University named after IP Shamyakin
Belarus
Belarus
O. V. Veko
Gymnasium, Kalinkovichi
Belarus
Belarus
V. M. Red’kov
B. I. Stepanov Institute of Physics of the National Academy of Sciences of Belarus, Minsk
Belarus
Belarus
References
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4. OvsiyukE. M., Red'kov V. M. // Mode of access: http://arxiv.org/abs/1109.0126.
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