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Relation Between Relativistic and Non-Relativistic Quantum Mechanics as Integral Transformation |
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| Authors: | R. M. Mir-Kasimov |
| Affiliation: | (1) Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow region, 141980, Russia;(2) Izmir Institute of High Technology, Izmir, 35437, Turkey |
| Abstract: | A formulation of quantum mechanics (QM) in the relativistic configurational space (RCS) is considered. A transformation connecting the non-relativistic QM and relativistic QM (RQM) has been found in an explicit form. This transformation is a direct generalization of the Kontorovich–Lebedev transformation. It is shown also that RCS gives an example of non-commutative geometry over the commutative algebra of functions. |
| Keywords: | relativistic non-relativistic configurational space non-commutative differential calculus Lorentz group representations Fourier transformation |
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