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
a Department of Metallurgy, Guizhou University of Technology, Guiyang 550003, China; b Department of Basic Science Guizhou University of Technology, Guiyang 550003, China
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.
Received: 17 June 2001
Revised: 22 July 2001
Accepted manuscript online:
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