Relation Between Relativistic and Non-Relativistic Quantum Mechanics as Integral Transformation
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Mir-Kasimov, Rufat M.
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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.
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Keywords
Configurational space, Fourier transformation, Lorentz group representations, Non-commutative differential calculus, Non-relativistic, Relativistic model, Fourier transformation, Non-commutative differential calculus, Non-relativistic, Relativistic model, Lorentz group representations, Configurational space
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Citation
Mir-Kasimov, R. M. (2002). Relation between relativistic and non-relativistic quantum mechanics as integral transformation. Foundations of Physics, 32(4), 607-626. doi:10.1023/A:1015088417135
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Q3
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Q2
OpenCitations Citation Count
7
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Foundations of Physics
Volume
32
Issue
4
Start Page
607
End Page
626
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CrossRef : 7
Scopus : 10
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345
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