Comparison of quasilinear and WKB approximations

Journal Article · Fri Dec 15 04:00:00 EST 2006 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2006.06.001· OSTI ID:20845949

Mandelzweig, V B ^[1]

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1. Racah Institute of Physics, Hebrew University, Jerusalem 91904 (Israel)

It is shown that the quasilinearization method (QLM) sums the WKB series. The method approaches solution of the Riccati equation (obtained by casting the Schroedinger equation in a nonlinear form) by approximating the nonlinear terms by a sequence of the linear ones, and is not based on the existence of a smallness parameter. Each pth QLM iterate is expressible in a closed integral form. Its expansion in powers of h reproduces the structure of the WKB series generating an infinite number of the WKB terms. Coefficients of the first 2 {sup p} terms of the expansion are exact while coefficients of a similar number of the next terms are approximate. The quantization condition in any QLM iteration, including the first, leads to exact energies for many well known physical potentials such as the Coulomb, harmonic oscillator, Poeschl-Teller, Hulthen, Hyleraas, Morse, Eckart, etc.

• OSTI ID: 20845949
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 12 Vol. 321; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COMPARATIVE EVALUATIONS
COULOMB FIELD
HARMONIC OSCILLATORS
INTEGRALS
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
POTENTIALS
QUANTIZATION
RICCATI EQUATION
SCHROEDINGER EQUATION
WKB APPROXIMATION