Phase-integral calculation of the energy levels of a quantal anharmonic oscillator

M. Lakshmanan, F. Karlsson, and P. O. Fröman
Phys. Rev. D 24, 2586 – Published 15 November 1981
PDFExport Citation

Abstract

The phase-integral method developed by N. Fröman and P. O. Fröman is used for solving the quantal eigenvalue problem of an anharmonic oscillator with quartic anharmonicity. The generalized Bohr-Sommerfeld quantization condition up to the seventh-order phase-integral approximation is expressed explicitly in terms of complete elliptic integrals. Solving this quantization condition numerically, and comparing the results with recent very accurate numerical results obtained by Banerjee, we present curves exhibiting in a general way the accuracies of various orders of the phase-integral approximations. These curves clearly illustrate the utility of higher-order phase-integral approximations for the treatment of anharmonic oscillators.

  • Received 12 June 1981

DOI:https://doi.org/10.1103/PhysRevD.24.2586

©1981 American Physical Society

Authors & Affiliations

M. Lakshmanan

  • Department of Physics, Autonomous Post-Graduate Center, University of Madras, Tiruchirapalli-620020, India

F. Karlsson and P. O. Fröman

  • Institute of Theoretical Physics, University of Uppsala, Thunbergsvägen 3, S-752 38 Uppsala, Sweden

References (Subscription Required)

Click to Expand
Issue

Vol. 24, Iss. 10 — 15 November 1981

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review D

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×