A summation method for the Rayleigh-Schrödinger series for the anharmonic oscillator

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

We approximate the energy levels of the anharmonic oscillator with any coupling constant by eigenvalues λj(g,T) of the operator - d2/dx2 + x2 + gVT(x) with V T(x) = x4 when |x|≤T and VT(x) = T 4 when |x| > T. The functions λj(g,T) are holomorphic with respect to g in a neighborhood of the non-negative half-axis. The conformal transformation maps this neighborhood onto the unit circle of the complex plane. It gives the summation method for the Rayleigh-Schrödinger series for every g>0.

Original languageEnglish (US)
Pages (from-to)961-964
Number of pages4
JournalJournal of Mathematical Physics
Volume26
Issue number5
DOIs
StatePublished - Jan 1 1985
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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