1994/12/12 by R. M. Kasimov, R. M. Mir -- Kasimov, Kasimov, R. M. Mir --
Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9412105
34 pages, REVTEX. Replaced for minor LATEX mistakes
openalex publication_date 1994/12/12 · arxiv created 1994/12/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The concept of the one -- dimensional quantum mechanics in the relativistic configurational space (RQM) is reviewed briefly. The Relativistic Schroedinger equation (RSE) arising here is the finite-difference equation with the step equal to the Compton wave length of the particle. The different generalizations of the Dirac -- Infeld -- Hall factorizarion method for this case are constructed. This method enables us to find out all possible finite-difference generalizations of the most important nonrelativistic integrable case -- the harmonic oscillator. As it was shown (\citekmn,\citemir6) in RQM the harmonic oscillator = q -- oscillator. It is also shown that the relativistic and nonrelativistic QM's are different representations of the same theory. Thetransformation connecting these two representations is found in explicit form. It could be considered as the generalization of the Kontorovich -- Lebedev transformation.