Communications in Theoretical Physics

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Notes on Application of WKB Method

GU Xiao-Yan1 and SUN Jian-Qiang2   


  1. 1 Department of Physics, East China University of Science and Technology, Shanghai 200237, China
    2 Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
  • Received: 2007-12-24 Revised: 2008-04-25 Published: 2008-10-15

Abstract: The notes here presented are of the modifications introduced in the application of WKB method. The problems of two- and three-dimensional harmonic oscillator potential are revisited by WKB and the new formulation of quantization rule respectively. It is found that the energy spectrum of the radial harmonic oscillator, which is reproduced exactly by the standard WKB method with the Langer modification, is also reproduced exactly without the Langer modification via the new quantization rule approach. An alternative way to obtain the non-integral Maslov index for three-dimensional harmonic oscillator is proposed.

Key words: WKB method, quantization rules, harmonic oscillator, two-dimensional space

PACS numbers: 

  • 03.65.Sq