The relativistic massless harmonic oscillator K. Kowalski and J. Rembieli´ nski Department of Theoretical Physics, University of GLYPH<suppress>L´ od´ z, ul. Pomorska 149/153, 90-236 GLYPH<suppress>L´ od´ z, Poland A detailed study of the relativistic classical and quantum mechanics of the massless harmonic oscillator is presented. PACS numbers: 03.30.+p, 03.65.-w, 03.65.Ge, 03.65.Pm 1 arXiv:1002.0474v1 [quant-ph] 2 Feb 2010 Abstract