Models of two-electron composite quantum systems

S. Vinitsky; A. Gusev; O. Chuluunbaatar; V. Derbov; A. Klombotskaya; A. Góźdź

doi:10.1117/12.2049714

30 January 2014 Models of two-electron composite quantum systems

S. Vinitsky, A. Gusev, O. Chuluunbaatar, V. Derbov, A. Klombotskaya, A. Góźdź

Proceedings Volume 9031, Saratov Fall Meeting 2013: Optical Technologies in Biophysics and Medicine XV; and Laser Physics and Photonics XV; 90311E (2014) https://doi.org/10.1117/12.2049714
Event: Saratov Fall Meeting 2013, 2013, Saratov, Russian Federation

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.

Citation Download Citation

S. Vinitsky, A. Gusev, O. Chuluunbaatar, V. Derbov, A. Klombotskaya, and 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); https://doi.org/10.1117/12.2049714

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