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arXiv:0812.2792 · Journal of Mathematical Chemistry

Combined theory of two- and four-component complete orthonormal sets of spinor wave functions and Slater type spinor orbitals in position, momentum and four-dimensional spaces

I. I. Guseinov

Published Aug 5, 2009• 3 citations
arXivHTMLPDF
DOI
10.1007/s10910-009-9582-9

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Using the complete orthonormal sets of radial parts of nonrelativitistic exponential type orbitals (2,1, 0, 1, 2, ...) and spinor type tensor spherical harmonics of rank s the new formulae for the 2(2s+1)-component relativistic spinors useful in the quantum mechanical description of the arbitrary half-integral spin particles by the generalized Dirac equation introduced by the author are established in position, momentum and four-dimensional spaces, where 1/ 2, 3 / 2, 5 / 2, ... s = . These spinors are complete without the inclusion of the continuum. The 2(2s+1)component spinors obtained are reduced to the independent sets of two-component spinors defined as a product of complete orthonormal sets of radial parts of orbitals and twocomponent spinor type tensor spherical harmonics. We notice that the new idea presented in this work is the unified treatment of half-integral spin and scalar particles in position, momentum and four-dimensional spaces. Relations presented in this study can be useful in the linear combination of atomic orbitals approximation for the solution of different problems arising in the relativistic quantum mechanics when the orthonormal basis sets of relativistic exponential type spinor wave functions and Slater type spinor orbitals in position, momentum and four -dimensional spaces are employed.
New formulae for the 2(2s + 1)-component relativistic basis spinors useful for the quantum mechanical description of the arbitrary half-integral spin particles by the generalized Dirac equation introduced by the author are established in position, momentum and four-dimensional spaces, where s = 1/2, 3/2, 5/2, . . . . These spinors are reduced to independent sets of two-component spinors. The relations presented in this study can be useful in the linear combination of atomic orbital approximation for the solution of different problems arising in relativistic quantum mechanics when orthonormal basis sets of relativistic exponential-type spinor wave functions and Slater-type spinor orbitals in position, momentum and four-dimensional spaces are employed.