Abstract
A Kantorovich method for solving the multi-dimensional eigenvalue and scattering problems of Schrödinger equation is developed in the framework of a conventional finite element representation of smooth solutions over a hyperspherical coordinate space. Convergence and efficiency of the proposed schemes are demonstrated on an exactly solvable model of three identical particles on a line with pair attractive zero-range potentials below three-body threshold. It is shown that the Galerkin method has a rather low rate of convergence to exact result of the eigenvalue problem under consideration.
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Chuluunbaatar, O., Kaschiev, M.S., Kaschieva, V.A., Vinitsky, S.I. (2003). Kantorovich Method for Solving the Multi-dimensional Eigenvalue and Scattering Problems of Schrödinger Equation. In: Dimov, I., Lirkov, I., Margenov, S., Zlatev, Z. (eds) Numerical Methods and Applications. NMA 2002. Lecture Notes in Computer Science, vol 2542. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36487-0_45
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DOI: https://doi.org/10.1007/3-540-36487-0_45
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