Highly Accurate Analytic Presentation of Solution of the Schrödinger Equation

Details Highly Accurate Analytic Presentation of Solution of the Schrödinger Equation Highly Accurate Analytic Presentation of Solution of the Schrödinger Equation

2007-10-26

arxiv.org/abs/0710.5042v1

Physics

Mathematical Physics

2 pages, 1 figure, submission for the Proceedings of the International Conference on Hadron Physics, 30 Aug - 3 Sep 2007, Cana

Scientific paper

10.1007/s00601-008-0328-1

High-precision approximate analytic expressions for energies and wave functions are found for arbitrary physical potentials. The Schr\"{o}dinger equation is cast into nonlinear Riccati equation, which is solved analytically in first iteration of the quasi-linearization method (QLM). The zeroth iteration is based on general features of the exact solution near the boundaries. The approach is illustrated on the Yukawa potential. The results enable accurate analytical estimates of effects of parameter variations on physical systems.

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