Analytic presentation of a solution of the Schrödinger equation

E. Z. Liverts; E. G. Drukarev; R. Krivec; V. B. Mandelzweig

doi:10.1007/s00601-008-0328-1

Analytic presentation of a solution of the Schrödinger equation

E. Z. Liverts, E. G. Drukarev, R. Krivec, V. B. Mandelzweig

Racah Institute of Physics

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

High-precision approximate analytic expressions for energies and wave functions are found for arbitrary physical potentials. The Schrödinger equation is cast into the 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.

Original language	English
Pages (from-to)	367-370
Number of pages	4
Journal	Few-Body Systems
Volume	44
Issue number	1-4
DOIs	https://doi.org/10.1007/s00601-008-0328-1
State	Published - 2008

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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 the 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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AU - Krivec, R.

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PY - 2008

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N2 - High-precision approximate analytic expressions for energies and wave functions are found for arbitrary physical potentials. The Schrödinger equation is cast into the 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.

AB - High-precision approximate analytic expressions for energies and wave functions are found for arbitrary physical potentials. The Schrödinger equation is cast into the 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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Analytic presentation of a solution of the Schrödinger equation

Abstract

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