Nonlinear Phenomena in Complex Systems, 2012, Vol.15, No.3, pp.209-226

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2012, Vol.15, No.3, pp.209-226

Quasi-Plane Waves for a Particle with Spin 1/2 on the Background of Lobachevsky Geometry: Simulating of a Special Medium.
E. Ovsiyuk

In the paper complete systems of exact solutions for Dirac and Weyl equations in the Lobachevsky space H₃ are constructed on the base of the method of separation of the variables in quasi-cartesian coordinates. An extended helicity operator is introduced. It is shown that solution constructed when translating to the limit of vanishing curvature coincide with common plane wave solutions on Minkowski space going in opposite z-directions. It is shown the problem posed in Lobachevsky space simulates a situation in the flat space for a quantum-mechanical particle of spin 1/2 in a 2-dimensional potential barrier smoothly rising to infinity on the right.

Key words: Dirac and Weyl equations, Lobachevsky space, Minkowski space, quasi-plane wave

Full text: Acrobat PDF (241KB)