中国物理B ›› 2001, Vol. 10 ›› Issue (4): 277-281.doi: 10.1088/1009-1963/10/4/302

• GENERAL • 上一篇    下一篇

A GENERATION OF EXACTLY SOLVABLE ANHARMONIC SYMMETRIC OSCILLATORS

刘克家   

  1. Department of Metallurgy, Guizhou University of Technology, Guiyang 550003, China
  • 收稿日期:2000-09-12 修回日期:2000-12-06 出版日期:2005-07-11 发布日期:2005-07-11
  • 基金资助:
    Project supported by the National Natural Science Foundation of Guizhou Province of China (Grant No. 3021)

A GENERATION OF EXACTLY SOLVABLE ANHARMONIC SYMMETRIC OSCILLATORS

Liu Ke-jia (刘克家)   

  1. Department of Metallurgy, Guizhou University of Technology, Guiyang 550003, China
  • Received:2000-09-12 Revised:2000-12-06 Online:2005-07-11 Published:2005-07-11
  • Supported by:
    Project supported by the National Natural Science Foundation of Guizhou Province of China (Grant No. 3021)

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摘要： Using the ideas of supersymmetric quantum mechanics, we exactly solve a continuous family of anharmonic potentials, which are the supersymmetric partners of the linear harmonic oscillators. The family includes a series of potentials in which the excited-state energy is the same as that of the harmonic oscillators, but the ground-state energy can be any value lower than the excited states. The shape of the potential is variable, which includes the double-well and triple-well potentials. All the potentials obtained in this paper are free of singularities, and the supersymmetry of the solutions is unbroken.

Abstract: Using the ideas of supersymmetric quantum mechanics, we exactly solve a continuous family of anharmonic potentials, which are the supersymmetric partners of the linear harmonic oscillators. The family includes a series of potentials in which the excited-state energy is the same as that of the harmonic oscillators, but the ground-state energy can be any value lower than the excited states. The shape of the potential is variable, which includes the double-well and triple-well potentials. All the potentials obtained in this paper are free of singularities, and the supersymmetry of the solutions is unbroken.

Key words: anharmonic potential, double-well potential, exact solution

中图分类号:  (Solutions of wave equations: bound states)

  • 03.65.Ge