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.KeywordsEigenvalue ProblemGalerkin MethodHelium AtomIdentical ParticleHyperspherical HarmonicThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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