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Type: Artigo de periódico
Title: The Casimir operator of SO(1,2) and the Poschl-Teller potential: an AdS approach
Author: da Rocha, R
de Oliveira, EC
Abstract: We present and discuss some features of the anti-de Sitter spacetime, that is jointly with de Sitter and Minkowski is only, the unique maximal isotropic manifold. Among all possible lorentzian manifolds, we restrict our attention to the anti-de Sitter (AdS) spacetime, with metric diag(1,- 1, - 1). We start by presenting the conformal time metric oil AdS and we then show how we can obtain the Schrodinger formalism [1]. The Lie algebra so(1,2) is introduced and used to construct spin and ladder operators. After presenting the unitary representations, the AdS(1,2) spacetime is suitably parametrized and a representation of SO(1,2) is obtained, from which the Schrodinger equation with Poschl-Teller potential is immediately deduced. Finally, we discuss some relations between the relativistic harmonic oscillator and the Klein-Gordon equation, using the AdS(1,2) static frame. Possible applications of the presented formalism are provided.
Subject: Schrodinger equation
Poschl-Teller potential
spin and ladder operators
Cartan form
unitary representations
anti-de Sitter spacetime
hyperbolical coordinates
quantum mechanics
Country: México
Editor: Sociedad Mexicana De Fisica
Rights: aberto
Date Issue: 2005
Appears in Collections:Unicamp - Artigos e Outros Documentos

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