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8 August 2006 On an effective approximation of the Kantorovich method for calculations of a hydrogen atom in a strong magnetic field
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Abstract
A new effective method of calculating the wave functions of discrete and continuous spectra of a hydrogen atom in a strong magnetic field is developed based on the Kantorovich approach to the parametric eigenvalue problems in spherical coordinates. The two-dimensional spectral problem for the Schrodinger equation with fixed magnetic quantum number and parity is reduced to a spectral parametric problem for a one-dimensional equation for the angular variable and a finite set of ordinary second-order differential equations for the radial variable. A canonical transformation is applied to approximate the finite set of radial equations by means of a new radial equation describing an open channel. The rate of convergence is examined numerically and illustrated with a set of typical examples. The results are in good agreement with calculations by other authors.
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O. Chuluunbaatar, A. A. Gusev, V. L. Derbov, M. S. Kaschiev, V. V. Serov, T. V. Tupikova, and S. I. Vinitsky "On an effective approximation of the Kantorovich method for calculations of a hydrogen atom in a strong magnetic field", Proc. SPIE 6165, Saratov Fall Meeting 2005: Laser Physics and Photonics, Spectroscopy and Molecular Modeling VI, 61650B (8 August 2006); https://doi.org/10.1117/12.696845
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