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Highly Accurate Analytic Presentation of Solution of the Schr\"{o}dinger Equation

Mathematical Physics 2009-11-13 v1 High Energy Physics - Phenomenology math.MP

Abstract

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.

Keywords

Cite

@article{arxiv.0710.5042,
  title  = {Highly Accurate Analytic Presentation of Solution of the Schr\"{o}dinger Equation},
  author = {E. Z. Liverts and E. G. Drukarev and R. Krivec and V. B. Mandelzweig},
  journal= {arXiv preprint arXiv:0710.5042},
  year   = {2009}
}

Comments

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