Comparison of quasilinear and WKB approximations

V. B. Mandelzweig*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

It is shown that the quasilinearization method (QLM) sums the WKB series. The method approaches solution of the Riccati equation (obtained by casting the Schrödinger 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 ℏ reproduces the structure of the WKB series generating an infinite number of the WKB terms. Coefficients of the first 2p 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, Pöschl-Teller, Hulthen, Hyleraas, Morse, Eckart, etc.

Original languageEnglish
Pages (from-to)2810-2829
Number of pages20
JournalAnnals of Physics
Volume321
Issue number12
DOIs
StatePublished - Dec 2006

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