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.
Received: 12 September 2000
Revised: 06 December 2000
Accepted manuscript online:
PACS:
03.65.Ge
(Solutions of wave equations: bound states)
Fund: Project supported by the National Natural Science Foundation of Guizhou Province of China (Grant No. 3021)
Cite this article:
Liu Ke-jia (刘克家) A GENERATION OF EXACTLY SOLVABLE ANHARMONIC SYMMETRIC OSCILLATORS 2001 Chinese Physics 10 277
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