skip to main content

Title: An asymptotic expansion for energy eigenvalues of anharmonic oscillators

In the present contribution, we derive an asymptotic expansion for the energy eigenvalues of anharmonic oscillators for potentials of the form V(x)=κx{sup 2q}+ωx{sup 2},q=2,3,… as the energy level n approaches infinity. The asymptotic expansion is obtained using the WKB theory and series reversion. Furthermore, we construct an algorithm for computing the coefficients of the asymptotic expansion for quartic anharmonic oscillators, leading to an efficient and accurate computation of the energy values for n≥6. -- Highlights: •We derived the asymptotic expansion for energy eigenvalues of anharmonic oscillators. •A highly efficient recursive algorithm for computing S{sub k}{sup ′}(z) for WKB. •We contributed to series reversion theory by reverting a new form of asymptotic series. •Our numerical algorithm achieves high accuracy for higher energy levels.
Authors:
; ;
Publication Date:
OSTI Identifier:
22224223
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 337; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; ACCURACY; ALGORITHMS; ANHARMONIC OSCILLATORS; ASYMPTOTIC SOLUTIONS; CALCULATION METHODS; EIGENVALUES; ENERGY LEVELS; POTENTIALS