Quasi-plane waves for a particle with spin 1/2 on the background of Lobachevsky geometry: simulating of a special medium

Details Quasi-plane waves for a particle with spin 1/2 on the background of Lobachevsky geometry: simulating of a special medium Quasi-plane waves for a particle with spin 1/2 on the background of Lobachevsky geometry: simulating of a special medium

2012-03-19

arxiv.org/abs/1203.4288v1

Physics

Mathematical Physics

33 pages

Scientific paper

In the paper complete systems of exact solutions for Dirac and Weyl equations in the Lobachevsky space 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.

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