30 January 2014 Models of two-electron composite quantum systems
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Abstract
Aimed at applications to the photonics of composite two-electron quantum systems like a helium atom in hyper­ spherical coordinates, the boundary value problem (BVP) for a system of coupled self-adjoined 3D elliptic partial differential equations of the Schrodinger type with homogeneous third-type boundary conditions is formulated in coupled-channel adiabatic approach. The Kantorovich reduction of the problem to BVPs for ordinary second­-order differential equations (ODEs) with respect to functions of a single hyper-radial variable is implemented by expanding the solution over a set of surface (angular) functions that depend on the hyper-radial variable as a parameter. Benchmark calculations are presented by the example of the ground and first excited states of a Helium atom. The convergence of the results with respect to the number of the surface functions and their components is studied. The comparison with the known results is presented.
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S. Vinitsky, S. Vinitsky, A. Gusev, A. Gusev, O. Chuluunbaatar, O. Chuluunbaatar, V. Derbov, V. Derbov, A. Klombotskaya, A. Klombotskaya, A. Góźdź, A. Góźdź, } "Models of two-electron composite quantum systems", Proc. SPIE 9031, Saratov Fall Meeting 2013: Optical Technologies in Biophysics and Medicine XV; and Laser Physics and Photonics XV, 90311E (30 January 2014); doi: 10.1117/12.2049714; https://doi.org/10.1117/12.2049714
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