An improved discretization of Schrodinger-like radial equations

Abstract

A new discretization of the radial equations that appear in the solution of separable second order partial differential equations with some rotational symmetry (as the Schrodinger equation in a central potential) is presented. It cures a pathology, related to the singular behaviour of the radial function at the origin, that suffers in some cases the discretization of the second derivative with respect to the radial coordinate. This pathology causes an enormous slowing down of the convergence to the continuum limit when the two point boundary value problem posed by the radial equation is solved as a discrete matrix eigenvalue problem. The proposed discretization is a simple solution to that problem. Some illustrative examples are discussed.

arXiv comment21 pages, 12 figures

References in corpus (5)

• Renormalization of the Inverse Square Potential
• Mécanique quantique
• Stability of skyrmion textures and the role of thermal fluctuations in cubic helimagnets: a new intermediate phase at low temperature
• Quantum effects for the 2D soliton in isotropic ferromagnets
• Exact Soliton-like Solutions of the Radial Gross-Pitaevskii Equation

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• Stability of the skyrmion lattice near the critical temperature in cubic helimagnets
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