中国物理B ›› 2001, Vol. 10 ›› Issue (12): 1110-1112.doi: 10.1088/1009-1963/10/12/305

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NEW EXACTLY SOLVABLE SUPERSYMMETRIC PERIODIC POTENTIALS

周国利1, 刘克家2, 何力2, 伍玉娇2   

  1. (1)Department of Basic Science Guizhou University of Technology, Guiyang 550003, China; (2)Department of Metallurgy, Guizhou University of Technology, Guiyang 550003, China
  • 收稿日期:2001-06-17 修回日期:2001-07-22 出版日期:2001-12-15 发布日期:2005-06-12
  • 基金资助:
    Project supported by the Natural Science Foundation of Guizhou Province, China (Grant No. 20003021).

NEW EXACTLY SOLVABLE SUPERSYMMETRIC PERIODIC POTENTIALS

Liu Ke-jia (刘克家)a, He Li (何力)a, , Zhou Guo-li (周国利)b, Wu Yu-jiao (伍玉娇)a   

  1. a Department of Metallurgy, Guizhou University of Technology, Guiyang 550003, China; b Department of Basic Science Guizhou University of Technology, Guiyang 550003, China
  • Received:2001-06-17 Revised:2001-07-22 Online:2001-12-15 Published:2005-06-12
  • Supported by:
    Project supported by the Natural Science Foundation of Guizhou Province, China (Grant No. 20003021).

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摘要： Using the formalism of supersymmetric quantum mechanics, we give an exact solution for a family of one-dimensional periodic potentials, which are the supersymmetric partners of the potential proportional to the trigonometric function cos(2x) such that the Schr?dinger equation for this potential is named the Mathieu equation mathematically. We show that the new potentials are distinctly different from their original ones. However, both have the same energy band structure. All the potentials obtained in this paper are free of singularities.

Abstract: Using the formalism of supersymmetric quantum mechanics, we give an exact solution for a family of one-dimensional periodic potentials, which are the supersymmetric partners of the potential proportional to the trigonometric function cos(2x) such that the Schr?dinger equation for this potential is named the Mathieu equation mathematically. We show that the new potentials are distinctly different from their original ones. However, both have the same energy band structure. All the potentials obtained in this paper are free of singularities.

Key words: periodic potential, exact solution, Mathieu's equation, supersymmetric quantum mechanics

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

  • 03.65.Ge
02.30.Sa (Functional analysis) 03.65.Ta (Foundations of quantum mechanics; measurement theory)